SOLUTION: Please help solve: -2x+3y=-2 y=3x-3

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Question 124727: Please help solve:
-2x+3y=-2
y=3x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
-2x%2B3y=-2
y=3x-3



-2x%2B3%283x-3%29=-2 Plug in y=3x-3 into the first equation. In other words, replace each y with 3x-3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


-2x%2B9x-9=-2 Distribute


7x-9=-2 Combine like terms on the left side


7x=-2%2B9Add 9 to both sides


7x=7 Combine like terms on the right side


x=%287%29%2F%287%29 Divide both sides by 7 to isolate x



x=1 Divide




Now that we know that x=1, we can plug this into y=3x-3 to find y



y=3%281%29-3 Substitute 1 for each x


y=0 Simplify


So our answer is x=1 and y=0 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+%28-2%2B2x%29%2F3%2C+3x-3%29+ Graph of -2x%2B3y=-2 (red) and y=3x-3 (green)