# How do you solve y=2x+9 and y=9x +10 using substitution?

Apr 26, 2018

$x = - \frac{1}{7}$ and $y = 8 \frac{5}{7}$

#### Explanation:

Take one y value and substitute it as the y value in the other equation.

Let's use $y = 2 x + 9$ to substitute in the other equation

$2 x + 9 = 9 x + 10$

Subtract 2x from both sides, then subtract 10 from both sides.

$9 = 7 x + 10$
$- 1 = 7 x$

Divide both sides by 7

$- \frac{1}{7} = x$

Now apply your new x value to the first equation, $y = 2 x + 9$

$y = \left(2 \cdot - \frac{1}{7}\right) + 9$
$y = - \frac{2}{7} + 9$
$y = 8 \frac{5}{7}$