# How do you solve the following system?:  3x + y = -1 , 2x – y = -4

May 28, 2018

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $y$:

$3 x + y = - 1$

$3 x - \textcolor{red}{3 x} + y = - 1 - \textcolor{red}{3 x}$

$0 + y = - 1 - 3 x$

$y = - 1 - 3 x$

Step 2) Substitute $\left(- 1 - 3 x\right)$ for $y$ in the second equation and solve for $x$:

$2 x - y = - 4$ becomes:

$2 x - \left(- 1 - 3 x\right) = - 4$

$2 x + 1 + 3 x = - 4$

$2 x + 3 x + 1 = - 4$

$\left(2 + 3\right) x + 1 = - 4$

$5 x + 1 = - 4$

$5 x + 1 - \textcolor{red}{1} = - 4 - \textcolor{red}{1}$

$5 x + 0 = - 5$

$5 x = - 5$

$\frac{5 x}{\textcolor{red}{5}} = - \frac{5}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - 1$

$x = - 1$

Step 3) Substitute $- 1$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = - 1 - 3 x$ becomes:

$y = - 1 - \left(3 \times - 1\right)$

$y = - 1 - \left(- 3\right)$

$y = - 1 + 3$

$y = 2$

The Solution Is:

$x = - 1$ and $y = 2$

Or

$\left(- 1 , 2\right)$