# How do you solve the following system?: x -9y =-2 , -2x +5y = -9

Apr 28, 2017

See the entire solution process below:

#### Explanation:

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

$x - 9 y = - 2$

$x - 9 y + \textcolor{red}{9 y} = - 2 + \textcolor{red}{9 y}$

$x - 0 = - 2 + 9 y$

$x = - 2 + 9 y$

Step 2) Substitute $- 2 + 9 y$ for $x$ in the second equation and solve for $y$:

$- 2 x + 5 y = - 9$ becomes:

$- 2 \left(- 2 + 9 y\right) + 5 y = - 9$

$\left(- 2 \cdot - 2\right) + \left(- 2 \cdot 9 y\right) + 5 y = - 9$

$4 - 18 y + 5 y = - 9$

$4 + \left(- 18 + 5\right) y = - 9$

$4 + \left(- 13\right) y = - 9$

$4 - 13 y = - 9$

$- \textcolor{red}{4} + 4 - 13 y = - \textcolor{red}{4} - 9$

$0 - 13 y = - 13$

$- 13 y = - 13$

$\frac{- 13 y}{\textcolor{red}{- 13}} = \frac{- 13}{\textcolor{red}{- 13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 13}}} y}{\cancel{\textcolor{red}{- 13}}} = 1$

$y = 1$

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

$x = - 2 + 9 y$ becomes:

$x = - 2 + \left(9 \cdot 1\right)$

$x = - 2 + 9$

$x = 7$

The solution is: $x = 7$ and $y = 1$ or $\left(7 , 1\right)$