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

May 25, 2017

See a solution process below:

#### Explanation:

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

$x - 2 y = - 5$

$x - 2 y + \textcolor{red}{2 y} = - 5 + \textcolor{red}{2 y}$

$x - 0 = - 5 + 2 y$

$x = - 5 + 2 y$

Step 2) Substitute $\left(- 5 + 2 y\right)$ for $x$ in the first equation and solve for $y$:

$2 x - 9 y = 5$ becomes:

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

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

$- 10 + 4 y - 9 y = 5$

$- 10 + \left(4 - 9\right) y = 5$

$- 10 + \left(- 5\right) y = 5$

$- 10 - 5 y = 5$

$\textcolor{red}{10} - 10 - 5 y = \textcolor{red}{10} + 5$

$0 - 5 y = 15$

$- 5 y = 15$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{15}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} y}{\cancel{\textcolor{red}{- 5}}} = - 3$

$y = - 3$

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

$x = - 5 + 2 y$ becomes:

$x = - 5 + \left(2 \cdot - 3\right)$

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

$x = - 11$

The solution is: $x = - 11$ and $y = - 3$ or $\left(- 11 , - 3\right)$