# How do solve the following linear system?:  5x-5y=10 , -4x-14y=28 ?

Feb 9, 2017

See the entire solution process below:

#### Explanation:

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

$5 x - 5 y = 10$

$5 x - 5 y + \textcolor{red}{5 y} = 10 + \textcolor{red}{5 y}$

$5 x - 0 = 10 + 5 y$

$5 x = 10 + 5 y$

$\frac{5 x}{\textcolor{red}{5}} = \frac{10 + 5 y}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = \frac{10}{\textcolor{red}{5}} + \frac{5 y}{\textcolor{red}{5}}$

$x = 2 + y$

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

$- 4 x - 14 y = 28$ becomes:

$- 4 \left(2 + y\right) - 14 y = 28$

$- 8 - 4 y - 14 y = 28$

$\textcolor{red}{8} - 8 - \left(4 + 14\right) y = \textcolor{red}{8} + 28$

$0 - 18 y = 36$

$- 18 y = 36$

$\frac{- 18 y}{\textcolor{red}{- 18}} = \frac{36}{\textcolor{red}{- 18}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 18}}} y}{\cancel{\textcolor{red}{- 18}}} = - 2$

$y = - 2$

Step 3) Substitute $- 2$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = 2 + y$ becomes:

$x = 2 + \left(- 2\right)$

$x = 0$

The solution is: $x = 0$ and $y = - 2$