# How do you solve 2x + 3y = 6 and x + 2y = 5?

Nov 21, 2015

$x = - 3$, $y = 4$.

#### Explanation:

From the second equation, you know that $x = 5 - 2 y$. Substitute this expression for $x$ in the first equation to get

$2 \left(5 - 2 y\right) + 3 y = 6$

$10 - 4 y + 3 y = 6$

$- y = - 4$

$y = 4$

Now that we have found $y$, we can find $x$ using

$x = 5 - 2 y \to x = 5 - 2 \cdot 4 = - 3$