# How do you solve x + 2y = 7 and 2x - 3y = -5?

Jun 5, 2016

You could solve using substitution.

#### Explanation:

$x + 2 y = 7$
$2 x - 3 y = - 5$

We can take one of these equations and solve for one variable, and plug that into the variable in the other equation. Let's use the first equation.

$x + 2 y = 7$ (We are solving for x)
$x = 7 - 2 y$ (We now have $x$, so we can plug this into $x$ in the other equation)

$2 x - 3 y = - 5$
$2 \left(7 - 2 y\right) - 3 y = - 5$ (Plug in $7 - 2 x$ from the other equation)
$14 - 4 y - 3 y = - 5$ (Distribute)
$- 7 y = - 19$
$y = \frac{19}{7}$ (We have the solution for $y$, time to find $x$)

$x + 2 \left(\frac{19}{7}\right) = 7$ (Plug in $y$)
$x + \frac{38}{7} = 7$
$x = \frac{11}{7}$ (We have the x value)

The solutions are: $x = \frac{11}{7}$, and $y = \frac{19}{7}$.