Question 298834
In the problem 3x+4y=6 5x+2y=-4  how do you know that you need to multiply by -2?
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3x+4y=6 
5x+2y=-4
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Multiplying eqn 2 by -2 will give -4 for the coefficient of y.  Then you can add and eliminate the y terms.
That's not the only way to do it, tho.
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You can multiply eqn 1 by 5 and eqn2 by 3, then subtract one from the other and eliminate x.  The x -2 is the simplest and easiest way (using elimination).
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Back to your question:  how do you know that you need to multiply by -2?
The answer is, you don't HAVE TO  multiply by -2.