Question

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

Answer 1

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`