# How do you solve systems of equations by solution 2x-3y=-1 and y=x-1?

##### 1 Answer
Mar 21, 2018

$x = 1$ and $y = - 1$

#### Explanation:

$2 x - 3 y = - 1 \text{ " " } \left(1\right)$

$y = x - 1 \text{ " " } \left(2\right)$

$\left(2\right)$ can be written as

$x - y = 1$

Therefore

$x - y = 1 \text{ }$ (multiply by $2$)

$2 x - 2 y = 2 \text{ " " } \left(3\right)$

So, $\left(1\right) - \left(3\right)$

$2 x - 3 y = - 1$
$- 2 x + 2 y = 2$

$- y = 1$

Therefore

$y = - 1$

Now substitute the value of $y$ in $\left(1\right)$

$2 x - 3 \left(- 1\right) = 1$

$2 x + 3 = 1$

$2 x = 3 - 1$

$x = \frac{2}{2}$

$x = 1$

Therefore

$x = 1$ and $y = - 1$