# How do solve the following linear system?:  -10x+7y=-2 , x-y=11 ?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

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

$x - y + \textcolor{red}{y} = 11 + \textcolor{red}{y}$

$x - 0 = 11 + y$

$x = 11 + y$

Step 2) Substitute $11 + y$ for $x$ in the first equation and solve for $y$:

$- 10 x + 7 y = - 2$ becomes:

$- 10 \left(11 + y\right) + 7 y = - 2$

$- 110 - 10 y + 7 y = - 2$

$- 110 - 3 y = - 2$

$- 110 + \textcolor{red}{110} - 3 y = - 2 + \textcolor{red}{110}$

$0 - 3 y = 108$

$- 3 y = 108$

$\frac{- 3 y}{\textcolor{red}{- 3}} = \frac{108}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} y}{\cancel{\textcolor{red}{- 3}}} = - 36$

$y = - 36$

Step 3) Substitute $- 36$ for $y$ in the solution to the second equation at the end of Step 1 and solve for $x$:

$x = 11 + y$ becomes:

$x = 11 - 36$

$x = - 25$

The solution is: $x = - 25$ and $y = - 36$