# Graph Linear Equations

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```					                     Graph Linear Equations
Graph Linear Equations

What is a linear equation: An equation is a condition on a variable. A variable takes on
different values; its value is not fixed. Variables are denoted usually by letter of alphabets,
such as x, y , z , l , m , n , p etc. From variables we form expression.

A linear equation is an algebraic equation in which each term is either a constant or the
product of a constant and (the first power of) a single variable. Linear equations can have one
or more variables. Linear equations occur with great regularity in applied mathematics.

While they arise quite naturally when modeling many phenomena, they are particularly useful
since many non-linear equations may be reduced to linear equations by assuming that
quantities of interest vary to only a small extent from some "background" state. Linear
equations do not include exponents.

Linear equation in one variable: These are the type of equation which have unique (i.e, only
one and one ) solution. For example: 2 x + 5 = 0 is a linear equation in one variable.

Linear equation in two variable: An equation which can be put in the form ax+by+c=0, where
a, b, and c are real numbers, and a and b are not zero, is called linear equation in two
variables. For example: 3 x + 4 y = 8 which is a equation in two variables.
Know More About Independent Variable Examples

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Summary : A linear equation in two variable has infinitely many solutions.The graph of every
linear equation in two variable is a straight line.

Every point on the graph of a linear equation in two variable is a solution of the linear
equation. An equation of the type y = mx represents a line passing through the origin.

Linear equations in two variables

A common form of a linear equation in the two variables x and y is where m and b designate
constants. The origin of the name "linear" comes from the fact that the set of solutions of such
an equation forms a straight line in the plane.

In this particular equation, the constant m determines the slope or gradient of that line, and the
constant term "b" determines the point at which the line crosses the y-axis, otherwise known
as the y-intercept.

Since terms of linear equations cannot contain products of distinct or equal variables, nor any
power (other than 1) or other function of a variable, equations involving terms such as xy, x2,
y1/3, and sin(x) are nonlinear

Method 2: Graph method for linear equation in two variable.

The graph of every linear equation in two variables is a straight line. Every point on the graph
of a linear equation is a two variables is a solution of the linear equation. moreover, every
solution of the linear equation is a point on the graph of the linear equation

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Multiplying Binomials
Multiplying Binomials

Introduction for multiplication of two binomial : - Multiplication of two binomials is nothing
but multiplying factors. The multiplication of two Binomials is done with two binomials. The
general form to multiply two binomials the binomials should like (ax + b) (cx + d) where x is a
variable and a, b, c and d are constants. The FOIL Method is used to multiply two binomials.

Steps for Multiplication of Two Binomials

The steps for the multiplication of two binomials. They are following,

Step 1: First write the factors.

Step 2: Start to use FOIL method.

Step 3: Now take the first term from the first binomial and multiply it with the first term of the
second binomial.

Step 4: Take the first term of the first binomial and then multiply it with second term of the
second binomial.

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Step 5: Now take the second term of the first binomial and then multiply it with first term of the
second binomial.
Step 6: Take the second term of the first binomial and then multiply it with second term of the
second binomial.
Step 7: Add all the result which we got from step 2 to step 6.
Step 8: Combine like terms.

Multiplying Binomials Examples

Below you could see the example for multiplying binomials

Q : Multiply two binomials: (x+3) (x+5)
Sol : Step 1: Given, factors are (x+3) (x+5)

Step 2: This can be done by using FOIL Method.
Step 3: Multiply first term of first binomial with first term of the second binomial.

First => x × x => x2
Step 4: Multiply first term of first binomial with second term of the second binomial.

Outer => x × 5 => 5x
Step 5: Multiply second term of first binomial with first term of the second binomial.
Inner => 3 × x => 3x

Step 6: Multiply second term of first binomial with second term of the second binomial

Lasts => 3 × 5 => 15

Step 5: Now sum all solutions x2+5x+3x+15
Step 6: Now combine the like terms x2+8x+15. (5x + 3x = 8x)
Step 7: Multiplying two binomials for (x+3)(x+5) is x2+8x+15.

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Thank You

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