# How do you solve 2x – 2y = 2, y = 3x – 17 using substitution?

Mar 15, 2016

This is very simple to do since a variable is already isolated, which is what is necessary to solve a system by substitution.

#### Explanation:

$2 x - 2 y = 2 \to y = 3 x - 17$

$2 x - 2 \left(3 x - 17\right) = 2$

$2 x - 6 x + 34 = 2$

$- 4 x = - 32$

$x = 8$

Now, substituting 8 for x, we get:

$y = 3 \left(8\right) - 17$

$y = 24 - 17$

$y = 7$

Thus, the solution set is $\left\{8 , 7\right\}$. Remember: solution sets must always be presented in the form $\left\{x , y\right\}$!

Practice exercises:

1. Solve the following by substitution. Leave answers in fractional form when necessary.

a) $x + 2 y = - 4 , 2 x - 5 y = 6$

b) $2 x + 7 y = 11 , - 6 x + 3 y = 14$

Good luck!