# How do you find the solution set for x+9y=-1, 2x+4y=5?

Aug 6, 2015

$\left\{\begin{matrix}x = \frac{7}{2} \\ y = - \frac{1}{2}\end{matrix}\right.$

#### Explanation:

You could solve this system of equations by suing the substitution method.

To do that, use the first equation to write $x$ as a function of $y$

$x + 9 y = - 1$

$x = - 1 - 9 y$

Now use this expression in the second equation - this will get you the value of $y$

$2 x + 4 y = 5$

$2 \cdot \left(- 1 - 9 y\right) + 4 y = 5$

$- 2 - 18 y + 4 y = 5$

$- 14 y = 7 \implies y = \frac{7}{- 14} = \textcolor{g r e e n}{- \frac{1}{2}}$

FInally, use the value of $y$ to get the value of $x$

$x = - 1 - 9 \cdot \left(- \frac{1}{2}\right)$

$x = - 1 + \frac{9}{2} = \textcolor{g r e e n}{\frac{7}{2}}$