SOLUTION: which equation is bets use for the problem y=-x+6 and x-2y=-6

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Question 120342: which equation is bets use for the problem y=-x+6 and x-2y=-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system
x-2y=-6
y=-x%2B6



x-2%28-x%2B6%29=-6 Plug in y=-x%2B6 into the first equation. In other words, replace each y with -x%2B6. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x%2B2x-12=-6 Distribute


3x-12=-6 Combine like terms on the left side


3x=-6%2B12Add 12 to both sides


3x=6 Combine like terms on the right side


x=%286%29%2F%283%29 Divide both sides by 3 to isolate x



x=2 Divide




Now that we know that x=2, we can plug this into y=-1x%2B6 to find y



y=-1%282%29%2B6 Substitute 2 for each x


y=4 Simplify


So our answer is x=2 and y=4 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+%28-6-x%29%2F-2%2C+-x%2B6%29+ Graph of x-2y=-6 (red) and y=-x%2B6 (green)