SOLUTION: Solve each system by substitution or addition, whichever is easier. 52. 2y – x = 3 x = 3y - 5

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve each system by substitution or addition, whichever is easier. 52. 2y – x = 3 x = 3y - 5       Log On


   

Question 165085: Solve each system by substitution or addition, whichever is easier.
52. 2y – x = 3
x = 3y - 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to use substitution to solve the system.


Start with the given system
2y-x=3
x=3y-5



2y-%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 (you have to solve for "y" for each equation first), we can see that their intersection is at . So this verifies our answer.


Graph of 2y-x=3 (red) and x=3y-5 (green)