SOLUTION: can someone help me with this problem x=2y-7 3x+2y=-5

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Question 131365: can someone help me with this problem
x=2y-7
3x+2y=-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
3x%2B2y=-5
x=2y-7



3%282y-7%29%2B2y=-5 Plug in x=2y-7 into the first equation. In other words, replace each x with 2y-7. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


6y-21%2B2y=-5 Distribute


8y-21=-5 Combine like terms on the left side


8y=-5%2B21Add 21 to both sides


8y=16 Combine like terms on the right side


y=%2816%29%2F%288%29 Divide both sides by 8 to isolate y



y=2 Divide




Now that we know that y=2, we can plug this into x=2y-7 to find x



x=2%282%29-7 Substitute 2 for each y


x=-3 Simplify


So our answer is x=-3 and y=2 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+%28-5-3x%29%2F2%2C+%28x%2B7%29%2F2%29+ Graph of 3x%2B2y=-5 (red) and x=2y-7 (green)