Solving a Systems of Equations by Elimination

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To solve a system of equations by addition or subtraction (or elimination), you must eliminate one of the variables so that you could solve for one of the variables. First, in this equation, you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero. However, this equation does not have any equal terms. So instead we will multiply one or both equations by a number so that they will equal each other resulting in elimination. In this equation we will want to manipulate both equations so that the y’s will both equal –6 (I chose –6 because it is a common term among –2 and –3). Multiply the WHOLE top equation by 3 to equal –6y (you have to multiply 7, -2, and 4 by 3. The outcome of the other two numbers will not matter to the overall equation.) Then multiply the bottom by 2 to equal –6 as well. Again, you have to multiply 2 to the WHOLE equation. Once you finish manipulating the equations you can now eliminate the y variable and only solve for x. If you subtract the -6y’s you must subtract the other numbers from each other as well. After you solve for x, plug it in to any one equation and then solve for y.
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