Substitution

Solving Systems of Equation by Substitution


 * How Substitute: **

4x+y=11 x+2y=8

To be able to solve for Y isolate Y.

y=11-4x

Once you have Y, you can substitute into the other equation

x+2(11-4x)=8

First Subtract 8x by x and transverse 22 to the right side:

x+22-8x=8

Subtract

-7x=8-22

Divide both sides by -7 to cancel 7 and leave x:

-7x=-14

Now you your answer: x=2

Once you have X, X can be used to solve for Y Now replace x with with your answer from the previous equation:

y=11-4(2)

Multiply 4 by 2 and subtract 11 by the answer:

y=11-8 ﻿﻿ y=3

Now you have your answer for Y

Now you have the final answer: x=2 y=3


 * Examples: **

1.) 3x+2y=2 (equation 1) y+8=3x (equation 2)

y=3x-8 3x=2(3x-8)=2 3x+6x-16=2 9x-16=2 9x=8 x=18/9 x=2 y=3(2)-8 FINAL: x=2 y=-2

2.) 3x-2y=12 (equation 1) y=4x+7 (equation 2)

3x-2y=12 (use equation 2 and substitute Y) 3x-2(4x+7)=12 (distribute 2 to 4x+7) 3x-8x-14=12 (put together similar terms) 3x-8x=12+14 (now solve all similar terms) -5x=26 (now divide -5x and 26 by -5) x=-5.2 (now solve for y)

3x-2y=12 (substitute x with the previous answer) 3(-5.2)-2y=12 -15.6-2y=12 (put together similar terms) -2y=12+15.6 (add similar terms) -2y=27.6 (now divide -2y and 27.6 by -2) y=-13.8

Answer: x=-5.2, y=-13.8