SOLUTION: Solve each system by substitution or addition. 2y-x=3 x=3y-5

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Question 121071: Solve each system by substitution or addition.
2y-x=3
x=3y-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2y-1x=3
x=3y-5



2y-1%283y-5%29=3 Plug in x=3y-5 into the first equation. In other words, replace each x with 3y-5. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


2y-3y%2B5=3 Distribute


-y%2B5=3 Combine like terms on the left side


-y=3-5Subtract 5 from both sides


-y=-2 Combine like terms on the right side


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



y=2 Divide




Now that we know that y=2, we can plug this into x=3y-5 to find x



x=3%282%29-5 Substitute 2 for each y


x=1 Simplify


So our answer is x=1 and y=2 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+%283%2Bx%29%2F2%2C+%28x%2B5%29%2F3%29+ Graph of 2y-1x=3 (red) and x=3y-5 (green)