SOLUTION: Solve using the multiplication principle first. Then use the elimination method: 7p+5q=2 8p-9q=17 I am not sure how to eliminate one of the factors. There is no common multip

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Question 377229: Solve using the multiplication principle first. Then use the elimination method:
7p+5q=2
8p-9q=17
I am not sure how to eliminate one of the factors. There is no common multiple of either P or Q. Please show me how to do this. Thanks.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Solve using the multiplication principle first.
Then use the elimination method:
:
7p + 5q = 2
8p - 9q = 17
:
We will eliminate q,
multiply the 1st equation by 9
multiply the 2nd equation by 5
:
63p + 45q = 18
40p - 45q = 85
-------------------adding eliminates q, find p
103p = 103
p =
p = 1
:
then use the 1st equation to find q, replace p with 1:
7(1) + 5q = 2
5q = 2 - 7
5q = -5
q =
q = -1
:
Check solutions in the 2nd equation
8(1) - 9(-1) = 17
8 + 9 = 17, confirms our solution
:
You can always use the coefficient of a variable in one equation
and multiply the same variable in the other equation, and vice versa
to eliminate the variable.
If the signs are different, add; If the signs are the same, subtract