SOLUTION: Hi I am having a problem solving this any help would be appreciated thank you in advance. I have to find the solution to the system of equations by the substitution method. this

Algebra ->  Systems-of-equations -> SOLUTION: Hi I am having a problem solving this any help would be appreciated thank you in advance. I have to find the solution to the system of equations by the substitution method. this      Log On


   

Question 144944This question is from textbook Toby Slater beginning Algebra
: Hi I am having a problem solving this any help would be appreciated thank you in advance.
I have to find the solution to the system of equations by the substitution method.
this is my problem:
#2 x=4- 4y
-x +2y = 2 This question is from textbook Toby Slater beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
-x%2B2y=2
x=4-4y



-%284-4y%29%2B2y=2 Plug in x=4-4y into the first equation. In other words, replace each x with 4-4y. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


-4%2B4y%2B2y=2 Distribute


6y-4=2 Combine like terms on the left side


6y=2%2B4Add 4 to both sides


6y=6 Combine like terms on the right side


y=%286%29%2F%286%29 Divide both sides by 6 to isolate y



y=1 Divide




Now that we know that y=1, we can plug this into x=4-4y to find x



x=4-4%281%29 Substitute 1 for each y


x=0 Simplify


So our answer is x=0 and y=1 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+%282%2Bx%29%2F2%2C+%28x-4%29%2F%28-4%29%29+ Graph of -x%2B2y=2 (red) and x=4-4y (green)