# How do you solve 3x+4y=-4 and x+2y=2 using substitution?

Jan 24, 2017

See the entire solution process below:

#### Explanation:

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

$x + 2 y = 2$

$x + 2 y - 2 y = 2 - 2 y$

$x + 0 = 2 - 2 y$

$x = 2 - 2 y$

Step 2) Substitute $\textcolor{red}{2 - 2 y}$ for $x$ in the first equation and solve for $y$:

$3 \left(\textcolor{red}{2 - 2 y}\right) + 4 y = - 4$

$6 - 6 y + 4 y = - 4$

$6 - 2 y = - 4$

$6 - 6 - 2 y = - 4 - 6$

$0 - 2 y = - 10$

$- 2 y = - 10$

$\frac{- 2 y}{\textcolor{red}{- 2}} = \frac{- 10}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} y}{\cancel{\textcolor{red}{- 2}}} = 5$

$y = 5$

Step 3) Substitute $\textcolor{red}{5}$ for $y$ in the solution to the second equation at the end of Step 1 and calculate $x$:

$x = 2 - \left(2 \times \textcolor{red}{5}\right)$

$x = 2 - 10$

$x = - 8$

The solution is:

$x = - 8$ and $y = 5$ or (-8, 5)