# How do you solve 3y - 2x = 11 and y + 2x = 9 using substitution?

Mar 10, 2018

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

#### Explanation:

$2 x + y = 9$
$- 2 x + 3 y = 11$

We need to solve $2 x + y = 9$ for $y$

$2 x + y = 9$
$y = 9 - 2 x$

Now substitute $- 2 x + 9$ for $y$ in $- 2 x + 3 y = 11$

$- 2 x + 3 y = 11$

$- 2 x + 3 \left(- 2 x + 9\right) = 11$

Distribute

$- 2 x + \left(3\right) \left(- 2 x\right) + \left(3\right) \left(9\right) = 11$

$- 2 x - 6 x + 27 = 11$

$- 8 x + 27 = 11$

$- 8 x = 11 - 27$

$- 8 x = - 16$

$x = \frac{- 16}{- 8}$

$x = 2$

Now substitute $2$ for $x$ in $y = - 2 x + 9$

$y = - 2 x + 9$

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

$y = - 4 + 9$

$y = 5$

Thus,

The answers are $y = 5$ and $x = 2$