SOLUTION: i am learning elimination using multiplication and i am really stuck i get everything i just dont get how you find the number that you have to multiply by this is the problem i n

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Question 247412: i am learning elimination using multiplication and i am really stuck i get everything i just dont get how you find the number that you have to multiply by
this is the problem i need help on
3x+2y=-9
x-y=-13
i dont know how you figure out which number you multiply the equation by can you please help me
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Every real number has a number called an additive inverse. The additive inverse is that number when added to the original number results in zero. The additive inverse of is because . The additive inverse of is . The additive inverse of is .

The name of the method gives us a clue. The goal of the elimination method is to eliminate one of the variables. A variable can be eliminated only when the coefficient on that variable in one equation is the additive inverse of the coefficient on that same variable in the other equation.

In your set, you have a 2 coefficient on in the first equation. What is the additive inverse of 2? The coefficient on in the second equation is -1. What would you have to multiply -1 by in order to make it the additive inverse of 2? The answer to that question is an answer to your question. It is just as correct as the other answer.

There is another answer to your question because there is nothing sacred about which variable you eliminate. Either one works and leads you to the exact same solution set.

If, instead of eliminating you wanted to eliminate , note that the coefficient on in the first equation is 3, so you have to change the second equation so that the coefficient on , currently 1, is the additive inverse of 3, namely -3.

Note that this particular problem is very straightforward. You only need to find one multiplier. Later down the road you will run into situations where you will need to find two multipliers. Thus:





Here, in order to eliminate , you need to multiply the first equation by 3 and the second equation by -7 (or -3 and 7 if you prefer -- doesn't matter in the end). And in order to eliminate you would multiply the first equation by 4 and the second equation by 5].

John