How do you solve the system 7x - 8y = 112 and y = -2x +9 by substitution?

May 28, 2015

You substitute the $y$-value of the second equation into the first:

$\to 7 x - 8 \cdot \left(- 2 x + 9\right) = 112$
$\to 7 x + 16 x - 72 = 112$
$\to 23 x = 184 \to x = \frac{184}{23} = 8$

Now put back the value of $x$ in the second equation:
$y = - 2 \cdot 8 + 9 = - 7$

So $x = 8 \mathmr{and} y = - 7$

$7 \cdot 8 - 8 \cdot \left(- 7\right) = 56 - \left(- 56\right) = 112$ check!