Question

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

Answer 1

Hint:

(Equation 1) - (Equation 2)

Answer 2

either multiply the first by 8 and the second by 7 and subtract the two new equations

or multiply the first by 9 and the second by 5 and add the two new equations

Answer 3

there's no need to solve for p and q individually, but you can if you want

Answer 4

7p + 5q = 2 -->(9)7p + 5q = 2
8p - 9q = 17 -->(5)8p - 9q = 17
--------------
63p + 45q = 18 (result of multiplying by 9)
40p - 45q = 85 (result of multiplying by 5)
--------------add
103p - 0 = 103
103p = 103
p = 1
now sub 1 in for p in either of the above equations
7p + 5q = 2
7(1) + 5q = 2
7 + 5q = 2
5q = 2 - 7
5q = - 5
q = -1
check...
7p + 5q = 2
7(1) + 5(-1) = 2
7 - 5 = 2
2 = 2 (correct)
Now we know that p = 1 and q = -1
-p + 14q
-1 + 14(-1)
-1 - 14 = - 15

Answer 5

Ah, I see what ya did there jim :D
I didn't even realize that. Yeah, just to what jimmy said!

Answer 6

Subtract the equations

7p + 5q = 2
8p - 9q = 17
------------
-p + 14q = -15

Answer 7

ohhh....thats a lot easier jim

Answer 8

7p + 5q = 2
-(8p - 9q = 17)
gives
-p + 14q = - 15

Answer 9

yes it is, but it only works if everything lines up perfectly (like it does conveniently here)

it's probably better to solve for p and q first, then evaluate like you did texaschic101

Answer 10

I should have used your way this time....it would have saved time

Answer 11

true, but you showed how to do it if things didn't match up like they did here

so it's good to see the more detailed explanation