Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters x and y as necessary.) 2x − 4y=46 −x + 2y=−23

Question

Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters x and y as necessary.)
2x − 4y = 46
−x + 2y = −23

Answer 1

Hi Porchae,

 

Substitution means replace. In order to use this method, you need to have either x=____ or y=_____. The first step is to choose one of the equations and solve for either x or y, whichever is easier. In the problem that you are trying to work on, I would recommend solving for x using the bottom equation, because x does not have a coefficient (numbers in front of the letter). 

 

Given -x+2y=-23, to solve for x, you need to move +2y to the other side by doing the opposite. Think of what would be the opposite of adding 2y and do that on both sides. After that you would have -x remain on the left side. To remove the negative sign, you can divide all terms by -1, or you can change all signs in the equation. So for example, if you have -x=3+2-1, it becomes x=-3-2+1.

 

After you solve for x using the second equation, you are going to use that to replace all the x you see in the first equation. So for example, if x=a+b, you first equation would be 2(a+b)-4y=46. 

 

Let me know if this helps or if you have any questions!

Answer 2

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