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

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) (Show Source): You can put this solution on YOUR website!

...........eq.1
..........eq.2
___________________________

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

...........eq.1.............multiply by
..........eq.2.............multiply by
___________________________
...........eq.1
..........eq.2
___________________________...............now subtract eq.2 from eq.1
...........eq.1
-
..........eq.2
_________________________________

now, go back to eq.1, plug in and solve for

...........eq.1

see it on a graph:

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