# How do you solve the system of equations y= - 2x + 6 and 2y + x = - 5?

Mar 7, 2017

See the entire solution process below:

#### Explanation:

Step 1) Because the first equation is already solved for $y$ we can substitute $- 2 x + 6$ for $y$ in the second equation and solve for $x$:

$2 y + x = - 5$ becomes:

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

$\left(2 \times - 2 x\right) + \left(2 \times 6\right) + x = - 5$

$- 4 x + 12 + x = - 5$

$- 4 x + x + 12 = - 5$

$- 3 x + 12 = - 5$

$- 3 x + 12 - \textcolor{red}{12} = - 5 - \textcolor{red}{12}$

$- 3 x + 0 = - 17$

$- 3 x = - 17$

$\frac{- 3 x}{\textcolor{red}{- 3}} = \frac{- 17}{\textcolor{red}{- 3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 3}}} x}{\cancel{\textcolor{red}{- 3}}} = \frac{17}{3}$

$x = \frac{17}{3}$

Step 2) Subsitute $\frac{17}{3}$ for $x$ in the first equation and calculate $y$:

$y = - 2 x + 6$ becomes:

$y = - \frac{34}{3} + \left(\frac{3}{3} \times 6\right)$

$y = - \frac{34}{3} + \frac{18}{3}$

$y = - \frac{16}{3}$

The solution is: $x = \frac{17}{3}$ and $y = - \frac{16}{3}$ or $\left(\frac{17}{3} , - \frac{16}{3}\right)$