SOLUTION: Use substitution to solve: x=3y-2,2x+4y=16

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Question 111723: Use substitution to solve: x=3y-2,2x+4y=16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system
2x%2B4y=16
x=3y-2



2%283y-2%29%2B4y=16 Plug in x=3y-2 into the first equation. In other words, replace each x with 3y-2. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


6y-4%2B4y=16 Distribute


10y-4=16 Combine like terms on the left side


10y=16%2B4Add 4 to both sides


10y=20 Combine like terms on the right side


y=%2820%29%2F%2810%29 Divide both sides by 10 to isolate y



y=2 Divide




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



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


x=4 Simplify


So our answer is x=4 and y=2


Since a solution exists, and it's unique, the system is consistent and independent