SOLUTION: What is the trick to solving this problem how do we know what number to multiply by to cancel out the X. 8X-7Y=-51 12X+13Y=41 We are not sure how to come up with the number to

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Question 883590: What is the trick to solving this problem how do we know what number to multiply by to cancel out the X.
8X-7Y=-51
12X+13Y=41
We are not sure how to come up with the number to break it down
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8x-7y=-51...........eq.1
12x%2B13y=41..........eq.2
___________________________

how do we know what number to multiply by to cancel out the x:
first look what are coefficients of the x in eq.1 and eq.2, you see these are 8 and 12
now, you know that 24 is divisible by 8 and by 12; so make it as common coefficients of the x in eq.1 and eq.2

8x-7y=-51...........eq.1.............multiply by 3
12x%2B13y=41..........eq.2.............multiply by 2
___________________________
24x-21y=-153...........eq.1
24x%2B26y=82..........eq.2
___________________________...............now subtract eq.2 from eq.1
24x-21y=-153...........eq.1
-
24x%2B26y=82..........eq.2
_________________________________
cross%2824x%29-cross%2824x%29-21y-26y=-153-82
-47y=-235
y=-235%2F-47
highlight%28y=5%29
now, go back to eq.1, plug in y=5 and solve for x

8x-7%2A5=-51...........eq.1
8x-35=-51
8x=-51%2B35
8x=-16
x=-16%2F8
highlight%28x=-2%29
see it on a graph:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+8x%2F7%2B51%2F7%2C+-12x%2F13%2B41%2F13%29+