# How do you solve 7x+ 6y=-23 and -9x+ y=47 using substitution?

May 27, 2016

$x = - 5 \mathmr{and} y = 2$

#### Explanation:

First, change the second equation to be $y = \ldots .$
So, we have the equations:

$7 x + 6 y = - 23 \text{ } \mathmr{and} y = 9 x + 47$

In the first equation, replace y by $\left(9 x + 47\right)$

$7 x + 6 \left(9 x + 47\right) = - 23$

$7 x + 54 x + 282 = - 23$

$61 x = - 305$

$x = - 5$

In the second equation, use $x = - 5$

$y = 9 \left(- 5\right) + 47 \Rightarrow y = 2$

Check for $x = - 5 \mathmr{and} y = 2$

$7 \left(- 5\right) + 6 \left(2\right)$
$- 35 + 12 = - 23$