# If 7p + 5q = 2 and 8p - 9q = 17, then what is -p + 14q?

Sep 22, 2015

I found $- 15$

#### Explanation:

Consider first your two initial equations forming a System:
$\left\{\begin{matrix}7 p + 5 q = 2 \\ 8 p - 9 q = 17\end{matrix}\right.$
Let us solve this system to find $p$ and $q$: to solve it let us multiply the first equation by $9$, the second by $5$ and add them together in columns:
$\left\{\begin{matrix}\textcolor{red}{9 \times} 7 p + 5 q = 2 \\ \textcolor{red}{5 \times} 8 p - 9 q = 17\end{matrix}\right.$

$\left\{\begin{matrix}63 p + 45 q = 18 \\ 40 p - 45 q = 85\end{matrix}\right.$ add them:
$103 p + 0 = 103$
so: $p = \frac{103}{103} = 1$
substituting into the first equation we get:
$7 + 5 q = 2$
$q = - 1$

Using these values of $p$ and $q$ into: $- p + 14 q$ you get:
$- 1 - 14 = - 15$