# How do you solve the system using elimination y = -x + 5 and 2x - 3y = -6?

Jun 3, 2015

$y = - x + 5$
$y + x = 5$.............equation $\left(1\right)$

$2 x \textcolor{red}{- 3 y} = - 6$...... equation $\left(2\right)$

multiplying equation $\left(1\right)$ by $3$
$\left(y + x = 5\right) \times 3$

$3 x \textcolor{red}{+ 3 y} = 15$........ equation $\left(3\right)$

Adding equations $\left(2\right)$ and $\left(3\right)$ to eliminate color(red)(3y:

$2 x \cancel{- 3 y} = - 6$
$3 x + \cancel{3 y} = 15$

 5x = 9 , color(blue)(x = 9/5
Substituting $x$ in equation $\left(1\right)$ to find $y$
$y = - x + 5$
y = -9/5 + 5 = (-9+25)/5 , color(blue)(y = 16/5

The solution for the system of equations is color(blue)( x= 9/5 and y = 16/5