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Question 68777: Solve the system of equations using the addition (elimination) method.
If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is “no solution” or “infinitely many solutions.”
3x – 2y = 7
-9x + 6y = -21
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since you must use the addition method, you can simply add the two equations together to eliminate a variable. Before you do that, you must multiply the top equation by a certain factor, so either the x or y coefficient are equal but have a different sign. In this case, you can multiply the entire top equation by 3
3*(3x-2y)=3*(7)
which becomes
9x-6y=21 and when added to
-9x+6y=-21 the result becomes
0x+0y=0.
This means that any value of x and y can work, since anything multiplied by zero is zero, so there are an infinite amout of solutions. If you solved each equation for y and plotted their graphs, you would see that these two equations were the same.
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