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

Mar 12, 2016

The quickest way would be to subtract the second equation from the first

#### Explanation:

We have $2 x + 3 y = 9$
minus $2 x + y = 11$
leaves $\cancel{2 x} - \cancel{2 x} + 3 y - y = 9 - 11$
$2 y = - 2 \to y = - 1$
Now substitute that for $y$:
$2 x + \left(- 1\right) = 11 \to 2 x = 12 \to x = 6$

Check with the other equation:
$2 \times 6 + 3 \times \left(- 1\right) = 12 - 3 = 9$ check!