SOLUTION: Solve each of the following systems by substitution. 8. 3x – y = -15 x = y -7

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Question 124410: Solve each of the following systems by substitution.
8.
3x – y = -15
x = y -7






Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
3x-y=-15
x=y-7



3%28y-7%29-y=-15 Plug in x=y-7 into the first equation. In other words, replace each x with y-7. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


3y-21-y=-15 Distribute


2y-21=-15 Combine like terms on the left side


2y=-15%2B21Add 21 to both sides


2y=6 Combine like terms on the right side


y=%286%29%2F%282%29 Divide both sides by 2 to isolate y



y=3 Divide




Now that we know that y=3, we can plug this into x=y-7 to find x



x=%283%29-7 Substitute 3 for each y


x=-4 Simplify


So our answer is x=-4 and y=3 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+%28-15-3x%29%2F%28-1%29%2C+%28x%2B7%29%2F1%29+ Graph of 3x-y=-15 (red) and x=y-7 (green)