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Now Solving Linear Equations By Substitution Method

Solving Linear Equations By Substitution Method is among the easiest way to get the values of the unknown variables as seen in this video tutorial. Today, we are going to be solving three sets of equations by the method of substitution. Let’s take a look at the first examples.
Solving linear equations by substitution method
Solving linear equations by substitution method

y=3x

y=4+x

To solve this equation by the method of substitution, we should always make sure that at least one of the unknown variable must be defined and must be alone on one side of the equation. In the above-given example, the variable y is alone on one side of the equation in both equation 1 and 2.

since y has been defined as being equivalent to 3x in equation 1. we can easily get the value of x by rewriting equation 2 and replacing y by 3x as shown below

→ 3x=4+x

now collect like terms together

→3x-x=4

→2x=4

now divide both side of the equation by 2 to get the value of x

→x=2

we can now get the value of y by choosing any of the above equation and replacing x for 2

let’s choose equation 1

→y=3(2)

→y=6

Therefore the solution of this equation is at a point where x=2 and y=6

pt (2,6) 

this can be represented by the below graph

Solving Linear Equations By Substitution Method Example 1
Solving Linear Equations By Substitution Method Example 1

Lets Now Solve Example 2

 2y-2x=8

x-3y=12

To solve this kind of equation by substitution method, we need to make sure that either x or y is defined and stand alone on one side of the equation. In this case lets choose equation and make x stands alone on one side of the equation.

choosing x-3y=12

→x=12+3y

now we can rewrite equation 1 and replace every x by 12+3y

→2y-2(12+3y)=8

→2y-24-6y=8

now collecting like terms together.

2y-6y=8+24

→ -4y=32

now divide both sides of the equation by -4 to get the value of y

→y=-8

Now select either equation 1 or 2 and substitute y for -8 to get the value of x as shown below.

let’s choose equation 2 as x-3y=12

→x-3(-8)=12

→x+24=12

→x=12-24

→x=-12

The solution of this equation is at a point where x=-12 and y=-8 as shown in the below graph. pt(-12,-8)

Solving Linear Equations By Substitution Method Example 2
Solving Linear Equations By Substitution Method Example 2

Lets now solve for the third example.

x=3y-5

x+y=11

Looking at this equation, we could easily see that x has already been defined and stands alone on one side of equation 1. we can just go ahead to rewrite equation 2 and replacing every x by 3y-5

→3y-5+y=11

Now collecting like terms together

→3y+y=11+5

→4y=16 

Now divide both side of the equation by 4

→y=4

Now choose either equation 1 or 2 and replace every y by 4 to get the value of x, I will go ahead to choose equation 1

→x=3y-5

→x=3(4)-5

→x=12-5

→x=7

The solution of this equation is at a point where x=7 and y=7 pt (7,4)

This can be represented by the below graph

Solving Linear Equations By Substitution Method Example 3
Solving Linear Equations By Substitution Method Example 3

Substitution methodElimination Method

Check out more examples here

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