SOLUTION: y=x-7 2y-x=-10 what is the solution to the above system of equations ? thank you.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: y=x-7 2y-x=-10 what is the solution to the above system of equations ? thank you.      Log On


   

Question 198241: y=x-7
2y-x=-10
what is the solution to the above system of equations ?
thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2y-x=-10 Start with the second equation.


2%28x-7%29-x=-10 Plug in y=x-7 into the first equation. In other words, replace each y with x-7. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x-14-x=-10 Distribute


x-14=-10 Combine like terms on the left side


x=-10%2B14Add 14 to both sides


x=4 Combine like terms on the right side



Now that we know that x=4, we can plug this into y=x-7 to find y


y=x-7 Start with the first equation.


y=%284%29-7 Plug in x=4


y=-3 Subtract


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 of y=x-7 (red) and 2y-x=-10 (green)