SOLUTION: Solve the system of equations y=2x-10 and x-y=7

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Question 112108: Solve the system of equations y=2x-10 and 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
x-y=7
y=2x-10



x-%282x-10%29=7 Plug in y=2x-10 into the first equation. In other words, replace each y with 2x-10. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x-2x%2B10=7 Distribute


-x%2B10=7 Combine like terms on the left side


-x=7-10Subtract 10 from both sides


-x=-3 Combine like terms on the right side


x=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=3 Divide




Now that we know that x=3, we can plug this into y=2x-10 to find y



y=2%283%29-10 Substitute 3 for each x


y=-4 Simplify


So our answer is x=3 and y=-4