# How do you solve x – y = 3 and 2x + 2y = 2 using substitution?

May 1, 2017

See the solution process below:

#### Explanation:

Step 1) Solve the first equation for $x$:

$x - y = 3$

$x - y + \textcolor{red}{y} = 3 + \textcolor{red}{y}$

$x - 0 = 3 + y$

$x = 3 + y$

Step 2) Substitute $3 + y$ for $x$ in the second equation and solve for $y$:

$2 x + 2 y = 2$ becomes:

$2 \left(3 + y\right) + 2 y = 2$

$\left(2 \cdot 3\right) + \left(2 \cdot y\right) + 2 y = 2$

$6 + 2 y + 2 y = 2$

$6 + \left(2 + 2\right) y = 2$

$6 + 4 y = 2$

$- \textcolor{red}{6} + 6 + 4 y = - \textcolor{red}{6} + 2$

$0 + 4 y = - 4$

$4 y = - 4$

$\frac{4 y}{\textcolor{red}{4}} = - \frac{4}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} y}{\cancel{\textcolor{red}{4}}} = - 1$

$y = - 1$

Step 3) Substitute $- 1$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 3 + y$ becomes:

$x = 3 + \left(- 1\right)$

$x = 3 - 1$

$x = 2$

The solution is: $x = 2$ and $y = - 1$ or $\left(2 , - 1\right)$