# Solve the following simultaneous equations?

Oct 18, 2017

$p = 5 , q = - 2$

#### Explanation:

So, you have $\left[\begin{matrix}5 p - 2 q = 9 \\ 2 p + 5 q = - 8\end{matrix}\right]$

First we will remove the $p$s by multiplying each equation until the coefficients are the same.

$\left[\begin{matrix}5 p - 2 q = 9 \\ 2 p + 5 q = - 8\end{matrix}\right] \times \left[\begin{matrix}2 \\ 5\end{matrix}\right] = \left[\begin{matrix}10 p - 4 q = 18 \\ 10 p + 25 q = - 40\end{matrix}\right]$

$\left[\begin{matrix}10 p - 4 q = 18 \\ - \text{ } 10 p + 25 q = - 40\end{matrix}\right] = \left[- 29 q = 58\right]$

$q = \frac{58}{-} 29 = - 2$

Now we put our value for q into one of the original equations to get: $5 p - 2 \left(- 2\right) = 9$
$5 p + 4 = 9$
$5 p = 5$
$p = \frac{5}{5} = 1$

$p = 5 , q = - 2$