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

1 Answer
Sep 22, 2015

I found -15

Explanation:

Consider first your two initial equations forming a System:
{(7p+5q=2),(8p-9q=17):}
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:
{(color(red)(9xx)7p+5q=2),(color(red)(5xx)8p-9q=17):}

{(63p+45q=18),(40p-45q=85):} add them:
103p+0=103
so: p=103/103=1
substituting into the first equation we get:
7+5q=2
q=-1

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