# How do you solve the following system?: -1/2x+5y=-20 , -x+6y=7

Nov 28, 2015

Answer: $\left(- \frac{155}{2} , - \frac{47}{2}\right)$

#### Explanation:

Equation 1: $- \frac{1}{2} x + 5 y = - 20$

Equation 2: $- x + 6 y = 7$

Multiply equation 1 by $- 2$ to eliminate fraction
-2[-1/2x +5y =-20}] hArr $\textcolor{red}{x - 10 y = 40}$

Take equation 2, solve for $x$

$- x + 6 y = 7 \Leftrightarrow \textcolor{red}{6 y - 7 = x}$

Substitute $\textcolor{red}{6 y - 7 = x}$ into first equation

$\textcolor{red}{6 y - 7} - 10 y = 40$

$- 4 y = 47$

$\textcolor{b l u e}{y = - \frac{47}{4}}$

Substitute
$6 \left(- \frac{47}{4}\right) - 7 = x$

$- \frac{141}{2} - \frac{14}{2} = x$

$\textcolor{b l u e}{- \frac{155}{2} = x}$