# How do you solve the system of equations 8x - 8y = - 16 and - 2x + 4y = 14?

Apr 19, 2017

See the entire solution process below:

#### Explanation:

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

$8 x - 8 y = - 16$

$\frac{8 x - 8 y}{\textcolor{red}{8}} = - \frac{16}{\textcolor{red}{8}}$

$\frac{8 x}{\textcolor{red}{8}} - \frac{8 y}{\textcolor{red}{8}} = - 2$

$x - y = - 2$

$x - y + \textcolor{red}{y} = \textcolor{red}{y} - 2$

$x - 0 = y - 2$

$x = y - 2$

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

$- 2 x + 4 y = 14$ becomes:

$- 2 \left(y - 2\right) + 4 y = 14$

$\left(- 2 \cdot y\right) - \left(- 2 \cdot 2\right) + 4 y = 14$

$- 2 y + 4 + 4 y = 14$

$4 y - 2 y + 4 = 14$

$\left(4 - 2\right) y + 4 = 14$

$2 y + 4 = 14$

$2 y + 4 - \textcolor{red}{4} = 14 - \textcolor{red}{4}$

$2 y + 0 = 10$

$2 y = 10$

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

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

$y = 5$

Step 3) Substitute $5$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = y - 2$ becomes:

$x = 5 - 2$

$x = 3$

The solution is: $x = 3$ and $y = 5$ or $\left(3 , 5\right)$