Area and Perimeter of a Concave Polygon

Area and Perimeter of a Concave Polygon

Unlike a regular polygon, there is no easy formula for the area of an irregular polygon. Each side could be a different length, and each interior angle could be different.

so we have to split concave polygon as triangles or parallelograms or other shapes that easy to find area . here is the example on how to calculate the area of concave polygon. in this example we could not directly find the formula for finding area but we can split this concave polygon as two parallelogram then we could find area easily by using formula for area of parallelogram .
* The perimeter of any polygon is the total distance around the outside.
* which can be found by adding together the length of each side.

I hope the above explanation was useful, now let us study words with x in them

Explain Ration in math

Let us study How to do ratios,

Definition for ratios:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example: For every Spoon of sugar, you need 2 spoons of flour (1:2)
I hope the above explanation was useful.

Math definitions for kids

Math definitions for kids:Addition means sum of two quantities. The sign used to do addition is ‘+ ‘.

If Joe has 2 black pencil and 3 blue pencil means then the total number of pencil is

2+3 that is 5 pencils.
Subtraction:

Subtraction means difference of two quantities. The sign used to do subtraction is ‘– ‘.

If Kayla has 5 rupees and she spent 2 rupees in a store then the amount she has left in a hand is 5-2 that is 3 rupees.
Division:

Division means sharing a number into equal parts. The sign used to do division is ‘/’.

If a mom has 6 chocolates and then if she wants to give those chocolates to 2 children means, then it is 6/2 that is 3 .So she will give 3 chocolates to each child.
Multiplication:

Multiplication means a number is added to itself a number of times. The sign used to do multiplication is ‘x’ or sometimes ‘*’.

2+2+2=6 which is same as 3 times 2 which is equal to 6.In maths we also learn multiplication with the help of time table chart.Hope you like the above example of Math definitions for Kids.Please leave your comments, if you have any doubts.

Percentage Change Calculator

Percentage Change Calculator:A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one.

The formula used to calculate the percentage change is Percentage change = [((V2 - V1) / (V1)) * 100] .

V1- represents the old value

V2 - the new one.There are many online calculators available for calculating percentage change.
Percentage Change Calculator - Example Problems:

Let us understand the meaning and example problems related to Percentage change calculator - Problem 1:-

Ram scored 86 runs in the cricket match on Monday. On Friday he scored 95 runs. Calculate the Percentage of change?

Solution:-

Given

V2 = new value = 95 runs.

V1 = old value = 86 runs.

Percentage of change = ?.

The formula used to calculate the percentage change is

Percentage change = [((V2 - V1) / (V1)) * 100] .

By plugging in the given values in to the formula we get

Percentage change = [ (95 - 86) / (86) * 100] .

The difference between 95 and 86 is 9.

By plugging in it to the formula we get the answer as

= [9 / 86] * 100.

The fraction 9/ 86 gives us 0.1046.

=0.1046 * 100

=10.46

The percentage of change is 10.46.In the next Blog we will discuss about Radical calculator.Hope you like the above example of Percentage change calculator.Please leave your comments, if you have any doubts.

Factoring Trinomials Calculator

The equation or a function is in the structure of ax2+bx+c =0 (where a≠0, b, c are constants ) called as trinomials.We can also refer it as a quadratic function. An algebraic expressions which has 3 terms known as trinomials.The trinomials having highest power 2.The trinomials have the two roots. There are two ways to factor the trinomial according to the co-efficient of x2 . In the following section we are going to learn how to factor the trinomials by using trinomials calculator.Factor Trinomials Calculator Method 1:For factoring the trinomials we must know the below two methods.

Factor trinomial calculator Method 1:

If the coefficient of x2 is one. That is a=1.

x2+bx+c=(x-r1)(x-r2), In this r1 and r2 are the roots of the trinomial equation

(x - r1) and (x - r2) are the factors of the trinomial.In the Blogs to come we can learn about factoring polynomials calculator.Hope you like the above example of Factor Trinomial Calculator.Please leave your comments, if you have any doubts.

Factoring Quadratics

Factoring Quadratics:The explanation for factoring quadratics expressions,

Step 1: In the first step, the constant term must be identified.

Step 2: In the next step, the product term for the constant terms must be identified.

Step 3: Check whether the obtained product is equal to the sum of the co-efficient if x.

Step 4: Write the product of the obtained terms.Factors of 28 is one of the most commonly asked question under this topic.Hope you like the above example of factoring quadratic.Please leave your comments, if you have any doubts.

Parallelogram Definition

Let us learn about the Parallelogram Definition:Two diagonals in the figure which intersects at a particular point and lie in the interior part of parallelogram.When two pairs of the sides are opposite and they are parallel to each other.Then it is called as parallelogram .Now let us see about the parallelograms sides introduction.In parallelograms introduction, we can draw a pair of parallel lines. Draw another pair of parallel lines intersecting the former.Thus the parallelogram can be formed.Thus we can say that the pair of opposite sides of parallelogram is of equal length.Similarly we can also learn about other topics such as types of lines.Hope you like the above example of Parallelogram Definition.Please leave your comments, if you have any doubts.

How to find standard deviation

Let us learn how to find standard deviation.The variance is the measure of variability about the mean. To find standard deviation is the square root of average squared deviation from the mean.In the determination of variance, we find that the units of individual observations xi and the unit of their mean or [barx] are different from that of variance, since variance involves the sum of squares of (xi– [barx] ). The mean of a set of examination is expressed as positive (+ve) square-root of the variance and is called standard deviation. In order to find standard deviation the following formula is to be used.The formula for standard deviation is
σ = [sqrt((1/n)sum_(i=1)^n (x i - barx )^2)] . In find standard deviation usually denoted by σ.Hope you like the above example of how to find standard deviation.Please leave your comments, if you have any doubts.

Properties of exponents

Properties of Exponents:
The following properties are very essential in solving exponents,
1. Property for the product exponents with same base,

a^m * aⁿ = a^m+n, provided a b

2. Property of exponents with zero superscript,

a⁰ = 1, provided a 0

3. Property for exponemts in fraction form,

= a^m * a^-n , provided a 0

4. Property for exponents with whole superscript,
(ab)^m = a^m * b^m , provided a b
5. Property for exponents with negative superscript,

a^-m = provided a 0

6. Property for exponents with common superscript when the terms are in product,

(a^mb^mc^m) = (a*b*c)^m ,

(a^m/b^m) = ( )^m , provided a b

7. Property for exponents with radicals,

= x

(a^m)ⁿ= a^{mn
I hope the above explanation was useful, now let me explain about dividing radicals.}

Multiplying Radicals

Multiplying Radicals:The explanation to multiplying radicals is given below.There are mainly two laws are used. They are given below,Product law:

* Product law are also used in the radical expressions.
* By using the product law, if the given radical expressions are having the same index value means, then it can be multiplied.

Example: [root(4)(2)] [xx] [root(4)(3)] = [root(4)(6)]

Distributive law:

* Distributive law are also used in the radical expressions.
By using the distributive law, we have to multiply each and every terms.

Example: a (b + c) = ab +ac.The other key area of study is dividing radicals.Hope you like the above example of Multiplying Radicals.Please leave your comments, if you have any doubts.

Want to know about Basic Points Calculator

How many Triangles

How many triangles:A triangle is a geometrical figure formed by three lines, which intersect each other and which are not all concurrent.Let us now learn how many triangles are their altogether,Types of Triangle.There are three types of triangles they are: Equilateral triangle,Isosceles triangle and Scalene triangle.In equilateral triangle all the three sides are equal and all the angles are equal,in isosceles triangle two sides and their opposite angles are equal,in scalene all the three sides are not equal.While studying Triangles we usually come across congruent triangles too.Hope you like the above example of How many Triangles.Please leave your comments, if you have any doubts.

How to Measure Circumference of a Circle

Searching for circumference of a circle formula ? let me explain you how to find the circumference of a circle,

* Measure diameter. The diameter of a circle is the distance across a circle, through its center. It can be visualized as a straight line cutting the circle in half. For large circles like running paths, the diameter can be estimated.

* Consider radius. Radius is the distance from the center of a circle to any point on the circle. The radius of a circle is half its diameter. When diameter is too large to determine, estimate the radius. Then use simple math and multiply the radius by 2.

* Grasp pi. Pi is the ratio of the circumference of a circle to its diameter. Pi is called a constant in math. It is a number that does not change, no matter the size of the circle. The value of pi is usually rounded to 3.14.* Calculate circumference. Use simple math to multiply the diameter of the circle by pi. If a jogger estimated diameter of a circular path as 200 meters across, then circumference would be 200 times 3.14 or 628 meters.

* Verify units of measurement. The units for circumference are the same as the units for diameter. If diameter is measured in meters, report circumference in meters.

I hope the above explanation was useful.

TRINOMIAL SQUARES

Let us study about TRINOMIAL SQUARES,

A trinomial that is the the square of a Binomial is called a TRINOMIAL SQUARE. Trinomials that are perfect squares factor into either the square of a sum or the square of a difference. Recalling that (x + y)² = x² + 2xy + y² and (x - y)² = x² - 2xy + y², the form of a trinomial square is apparent. The first term and the last term are perfect squares and their signs are positive. The middle term is twice the product of the square roots of these two numbers. The sign of the middle term is plus if a sum has been squared; it is minus if a difference has been squared.

The polynomial 16x² - 8xy + x² is a trinomial in which the first term, 16x , and the last term, y², are perfect squares with positive signs. The square roots are 4x and y. Twice the product of these square roots is 2(4x)(y) = 8xy. The middle term is preceded by a minus sign indicating that a difference has been squared.

I hope the above explanation helped you.

Explain Concentric circles

Let us study about concentric circles,
In a large circle, two or more small circles inside a large circle and the center for all the circle inside is same. Other wise circle which have common center are known as concentric circle.

Wher R is the radius of the large circle, and r is the radius of the small circle.

In the figure we see that the center is same for both the circle.

For concentric circle we can find the area of ring inside large circle and small circle is given by.

Area of a ring = Area of large circle - area of small circle

= πR2 - πr2

= π(R+r)(R-r) Square units

Let us example for area of a ring in a concentric circle.

I hope the above explanation was useful, now let me explain how to find area of circle.

Statistics

Statistics:

The common question that is asked about any new topic is what is the meaning of that topic,similarly let us learn about what is Statistics??Statistics deals mainly in communicating facts and figures in terms of a method called statistical method. Collection, classification, tabulation, representation, reasoning, testing and drawing inferences are part of statistical methods.Rainfall patterns of a particular city over a period of time can be analyzed and a fair estimate about next season can be arrived at, with the help of figures (data) collected over a period of time.

The statistical method of studying a problem broadly consists of the following steps,basically we can get help on the statistical methods by following the steps given below:

* to collect numerical data about the problem,
* to present the collected data systematically,
* to analyze the data and
* to interpret the data and draw conclusions from it.

We have already learnt about the measures of central tendency, the mean, median and mode. Each of these gives a representative value of the data. If we say "the mean of a data is 15", we expect most of the values to be centered around 15. But measures of central tendency don't give us the complete picture. We would want to know how the values are scattered around the mean or the median. In other words, we want to study the variability and define a single number to describe the variability. This number is called the "measure of dispersion". Two of the measures of dispersion are Mean Deviation and Standard Deviation.We can also get help on statistics and probability by learning the statistics formulas.

Hope you like the above example of Statistics.Please leave your comments, if you have any doubts.

Area of Circle

Area of a Circle:

Draw a circle. Divide it into equal (even) sectors and arrange them in line as shown below.

This shape looks like a rectangle of length 'pr' and breath 'r' units
Let us now learn about the area of a circle in detail.
Area of the circle = Area of the rectangle

= length x breadth

= ∏ r x r

= ∏ r2 Sq. units
Next in this Blog let us look at the formula of the Areas of a circle.
Area of a circle Formula is ∏ r2 Sq. units

Area of a semicircle = 21 ∏ r2 Sq. units

Area of a quadrant = 41 ∏ r2 Sq. units.
The last topic that we will learn about in this area of the Circles Problems,and we will also see the various how we can solve these problems.
Problems related to area of A Circle:If the area of the sector of a circle is 60 sq. cm and the length of the arc of the sector is 12 cm, what is the radius of the circle?

Solution:
Area of the sector = 1 lr = 60 cm2
2

l = 12cm.
A = 1 x 12 x r = 60
2

6r = 60

r = 10 cm.

The radius of the circle is 10 cm.

Hope you like the above example of Area of a Circle.Please leave your comments, if you have any doubts.

Symmetry

Definition:-

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection. The second meaning of Symmetry is a precise and well-defined concept of balance or "patterned self-similarity" that can be demonstrated or proved according to the rules of a formal system: by geometry, through physics or otherwise.

In formal terms, we say that a mathematical object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation preserves some property of the object. The set of operations that preserve a given property of the object form a group. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations (and vice versa).

Types of Symmetry:

In this Blog I will also share with you the information on the different types of Symmetry.In the following two different types of symmetry are given:

1. Symmetry in geometry
2. Symmetry in mathematics


Symmetry in geometry:

Symmetry definition in geometry it means a sub-group.Our next concern is the very important topic on Isometrics,the most common question here is-What does Isometrics consists of?? Isometrics consists of three or two dimensional space. In following operations:

1. Reflectional Symmetry(FLIP)
2. Rotational Symmetry (TURN)
3. Translational Symmetry (SLIDE)

Reflectional symmetry (FLIP):

Splits the image into one side of the half side of mirror image. It is also called line or mirror symmetry. A Reflectional symmetry is called FLIP.

Rotational symmetry (TURN):

To turn the center point of an object into degress. A Rotational symmetry is called TURN.

Translational symmetry (SLIDE):

In straight line is divided into sequence line. A Translational symmetry is called SLIDE.

Symmetry in Mathematics

In mathematical operation, to apply the object into operation. The set of operations to form a group. Two object form a group of operations. To apply the objects into symmetry. So it is called a symmetry definition in mathematics.

Hope you like the above example of Symmetry.Please leave your comments, if you have any doubts.

Fractions

In this Blog I will help you understand the concept of Fractions and also we we see how to solve the fractions.Fraction is an equal part of one whole object.The most common question is how do you denote a fraction???Fraction can be represented as " p/q " where 'p' denotes the value called numerator and 'q' denotes the value called denominator and q not equal to zero.

Introduction to fraction:

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator.

In this Blog we are going to see how to change 385 to fraction and 385 into decimal,what is mean by improper fraction and some other examples based on fraction.

385 to Fraction:

385 to Fraction:

In this Blog we are going to see how to convert 385 to fraction and what is mean by improper fraction and how to convert 385 into decimal.Let us now solve few problems related to Fractions to understand the concept even better.

Problem 1:

Convert 385 to fraction.

Solution:

Given integer 385.

To convert the 385 to fraction we need to multiply and divide by the same number.We get only the improper fraction.

Improper fraction:

If [a/b] is improper fraction means, b < 10 =" [3850"> 38.5 × 10

(ii) 385 × (100/100)

=> 3.85 × 100

=> 3.85 × 102

(iii) 385 × (1000/1000)

=> 0.385 × 1000

=> 0.385 × 103

Problems on Fraction:

Problem1:

Add two fraction [3/4] and [2/5]

Solution:

Given , [3/4] and [2/5]

= [3/4] + [2/5]

To add fraction ,we need common denominator,

To make a common denominator , multiply 3/4 by 5 on both numerator and denominator and multiply 2/5 by 4 on both numerator and denominator.

= [3/4] × [5/5] + [2/5] × [4/4]

= [15/20 ] + [8/20]

= [(15+8) / 20]

= [23 /20]

Answer: [3/4] + [2/5] = [23 /20]

Problem 2:

Multiply the fractions 5/6 and 2/8

Solution:

Given, [5/6] and [2/8]

= [ 5/6] × [2/8]

= [ ((5)(2)) / ((6)(8))]

= [10/48]

= [5 / 24]

Answer: [5 / 24]

Problem 3:

[Divide the fraction 16/25 by 10/24]

Solution:

Given, [16/25] ÷ [10 /24]

We can divide by,

(i) Take the reciprocal for [10/24]

(ii) Multiply it with [16/25]

[16/25] ÷ [10 /24] = [16 /25] × [ 24 /10]

= [((16)(24)) / (( 25)(10))]

= [ 384 / 250 ]

= [192 / 125]

Answer: [192 / 125]

Hope you like the above example of Fractions.Please leave your comments, if you have any doubts.

Volume of Cone

Volume of Cone:
In general terms when we speak about a cone the first thing that comes to our mind is an ice-cream cone as depicted in the picture on the right hand side.

But to be more specific the meaning of a cone is given below "A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.n geometry, there are two types of shapes." They are two dimensional and three dimensional.

Two dimensional shapes are rectangle, square, parallelogram, rhombus etc.

Three dimensional shapes are cone, sphere, pyramid, cube, prism.


Properties of cone:

There are two properties of cone . They are volume of cone, surface area of cone. By using the properties of cone, we can calculate volume and surface area.

A cone has radius (r) and height (h) , slant height (s).

Volume of cone V = 1/3 * π * radius2 * height where π = 3.14

Volume of cone V = 1/3 * Volume of cylinder

Surface area of cone SA = π*radius* [sqrt(radius^2+height^2)]

Total surface area of cone = Surface area + π*radius2.

In this blog we will also see some example problems related to Volume of a cone.By solving few problems we can understand how to calculate the surface of a cone.
Problem 1:

Find the volume of cone for the radius = 1 meter and height = 1 meter.

Solution:

Given radius = 1 meter

Height = 1 meter

Volume of cone = [1/3] * π * radius2 * height

= [1/3 ] * 3.14 * (1)2 * (1)

= [1/3] * 3.14 * 1 * 1

= [3.14/3]

= 1.05 m3.

Problem 2:

Find the Total Surface area of cone for the radius is 3 meter and height is 4 meter.

Solution:

Given: Radius = 3 m

Height = 4 m

Surface area of cone = π*radius* [sqrt(radius^2+height^2)]

= 3.14 * 3 * [sqrt(3^2+4^2)]

= 3.14 * 3 * [sqrt(9+16)]

= 3.14 * 3 * [sqrt(25)]

= 3.14 * 3 * 5

= 47.1 m2.

Total surface area of cone = Surface area + π*radius2.

= 47.1 + 3.14*32

= 47.1 + 3.14 * 9

= 47.1 + 28.26

= 75.36 m2.

Problem 3:

Find the height of a cone for the volume of cone is 100 cubic inches and radius of a cone is 5 inches.

Solution:

Given: Volume of cone V = 100 cubic inches

Radius of cone = 5 inches

Volume of cone = [1/3 ] * π * radius2 * height

100 = [ 1/3 ] * π * 52 * height

100 = [1/3] * 3.14 * 25 * height

100 = [1/3] * 3.14 * 25 * height

100 = [(3.14*25)/3] *height

100 = [78.5/3] *height

100 = 26.17 * height

Height = [100/26.17]

Height = 3.82 inches

Hope you like the above example of Surface area of cone.Please leave your comments, if you have any doubts.

Coordinate Planes

Coordinate Plane:

In this Blog before we get into the details of coordinate planes,let us first understand the definition of a coordinate plane.The basic meaning of a coordinate plane is Coordinate plane is a plane formed by the intersection of a horizontal number line.

Definition of Coordinate Plane:

Coordinate plane is a plane formed by the intersection of a horizontal number line with a vertical number line. They intersect at their zero points. This point of intersection is called the origin and written as (0, 0).

On a coordinate plane, the horizontal number line is called the x-axis and the vertical number line is called the y-axis.

This is a coordinate plane. It has two axes and four quadrants. The two number lines form the axes. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. The center of the coordinate plane is called the origin. It has the coordinates of (0,0). Locations of points on the plane can be plotted when one coordinate from each of the axes are used. This set of x and y values are called ordered pairs.




















With the help of another example we can get a clear understanding about the coordinate Planes.


In the coordinate plane there are four quadrants.

Quadrant 1.

In quadrant 1 both X axis and Y axis values are positive. [( +x, +y )]

Quadrant 2

In quadrant 2 X axis values are negative and Y axis values are positive. [( - x, +y )]

Quadrant 3

In quadrant 3 X axis values are positive and Y axis values are negative. [( + x, - y )]

Quadrant 4

In quadrant 4 both X axis and Y axis values are negative. [( - x, - y )]
Hope you like the above example of Coordinate Planes.Please leave your comments, if you have any doubts.

Prime Numbers

Prime Numbers:

Introduction to meaning of Prime Numbers:
We are often faced with the questions like-What is the meaning of Prime numbers??In mathematics, a prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. The first twenty-five prime numbers are: Prime Numbers:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.Condition: - If x is the prime number then the next factors of the number x is 1 and X. Let us now see the meaning of prime numbers.A prime number is one that has only two factors namely 1 and itself and a composite number has factors besides 1 and itself.



In this blog we can get a clear understanding of Prime Numbers.A natural number greater than 1 that has no divisor between 1 and itself is said to be prime, hence called a prime number or simply a prime. Every natural number greater than 1 has at least the two distinct divisors 1 and itself; a prime has no others.

The number 2 is a prime, there being no candidate divisors between 1 and itself; from it, all even numbers thereafter are non-prime, i.e. 50% of all subsequent numbers. The numbers 3, 5, and 7 are all prime, meaning that, of the first six such subsequent numbers, precisely half are prime, half non-prime. However, of any subsequent six consecutive numbers, at least one of the odd values must be divisible by 3; including the three even numbers this means that at least 66% must be non-prime.So the trend goes; as we look further afield, with an accumulating collection of primes to be divisors, the density of primes declines progressively. But, no matter how far up the numbers we travel, we never exhaust the primes, nor is there any known point above which all further primes are spaced by more than the minimal value of 2 .

Example Problems - Meaning of Prime Numbers:

The easiest way to understand the prime numbers is by solving problems related to Prime numbers.

Problem 1:

Find out the number 29 is prime number or not?

Solution:

Here the number 29 is divisible by one and itself only. It has no more factors other than this. So 29 is considered as a prime number.

Problem 2:

Find out the number 53 is prime number or not?

Solution:

The getting number 53 is not divisible by two. 53 has only two factors. Those factors are one and itself only. So we can say the given number is prime number.

Hope you like the above example of Prime Numbers.Please leave your comments, if you have any doubts.

Introduction to Algebraic Fractions

Let us study about Algebraic Fractions,
Introduction to Algebraic Fractions :

Algebraic fractions are fractions using a variable in the numerator or denominator, such as 3/ x. Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0. Therefore, in the fractions
Be aware of these types of restrictions.
I hope the above explanation was useful.

The Binomial

The Binomial

A discrete variable that can result in only one of two outcomes is called binomial. For example, a coin flip is a binomial variable; but drawing a card from a standard deck of 52 is not. Whether a drug is either successful or unsuccessful in producing results is a binomial variable, as is whether a machine produces perfect or imperfect widgets.

Binomial experiments

Binomial experiments require the following elements:

* The experiment consists of a number of identical events ( n).
* Each event has only one of two mutually exclusive outcomes. (These outcomes are called successes and failures.)
* The probability of a success outcome is equal to some percentage, which is identified as a proportion, π.
* This proportion, π, remains constant throughout all events and is defined as the ratio of number of successes to number of trials.
* The events are independent.
* Given all of the above, the binomial formula can be applied ( x = number of favorable outcomes; n = number of events):
I hope the above explanation was useful.

Gaussian Elimination

Gaussian Elimination :

The purpose of this article is to describe how the solutions to a linear system are actually found. The fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Once this final variable is determined, its value is substituted back into the other equations in order to evaluate the remaining unknowns. This method, characterized by step-by-step elimination of the variables, is called Gaussian elimination.

Example 1: Solve this system:


Multiplying the first equation by −3 and adding the result to the second equation eliminates the variable x:


This final equation, −5 y = −5, immediately implies y = 1. Back-substitution of y = 1 into the original first equation, x + y = 3, yields x = 2. (Back-substitution of y = 1 into the original second equation, 3 x − 2 y = 4, would also yeild x = 2.) The solution of this system is therefore ( x, y) = (2, 1), as noted in Example 1.

Gaussian elimination is usually carried out using matrices. This method reduces the effort in finding the solutions by eliminating the need to explicitly write the variables at each step. The previous example will be redone using matrices.
Hope the above explanation was useful, now let me explain about matrices.