SOLUTION: In the problem 3x+4y=6 5x+2y=-4 how do you know that you need to multiply by -2?

Question 298834: In the problem 3x+4y=6 5x+2y=-4 how do you know that you need to multiply by -2?

Found 2 solutions by TX911, Alan3354:
Answer by TX911(36) (Show Source): You can put this solution on YOUR website!
Because when using the addition method:
3x+4y=6
5x+2y=-4
we need to solve for y first because if we solve for x first we're going to be dealing with fractions which we want to avoid in the interest of simplicity. So what do we need to multiply the second equation by in order to set the y's to where they cancel each other? That's right, -2 because 2*-2 =-4. Now when we add the top equations 4y to the bottom equations -4y we get zero which now let's us solve for y. Don't forget to multiply the other numbers in the second equation by -2 as well. It should look like -2(5x+2y=-4) and our result would be -10x-4y=-8.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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.
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