# How do you solve the system by graphing 3x – 6y = 12 and 9x + 2y = –24?

Aug 23, 2017

$x = - 2 \mathmr{and} y = - 3$

#### Explanation:

There is no single variable, so substitution is not a good method in this case. However, notice that the signs of the $y$terms are opposite. It will be easy to make the $y$-terms into additive inverses.

$\textcolor{w h i t e}{\times \times \times x} 9 x + 2 y = - 24 \textcolor{w h i t e}{\times \times \times \times} A$
$\textcolor{w h i t e}{\times \times \times x} 3 x \textcolor{red}{- 6 y} = + 12 \textcolor{w h i t e}{\times \times x . \times x} B$
$A \times 3 : \text{ } 27 x \textcolor{red}{+ 6 y} = - 72 \textcolor{w h i t e}{\times \times \times \times} C$
$B + C : \text{ } 30 x = \textcolor{w h i t e}{\times x} - 60$
$\textcolor{w h i t e}{\times \times \times \times} x = \textcolor{w h i t e}{\times \times} - 2$

Substitute $- 2 \text{ for } x$ in A
$\textcolor{w h i t e}{\times x} 9 \left(- 2\right) + 2 y = - 24$
$\textcolor{w h i t e}{\times \times} - 18 + 2 y = - 24$
$\textcolor{w h i t e}{\times \times \times \times \times} 2 y = - 24 + 18$
$\textcolor{w h i t e}{\times \times \times \times \times} 2 y = - 6$
$\textcolor{w h i t e}{\times \times \times \times \times x} y = - 3$