SOLUTION: solve using the substitution method y = 3 - x 2x + 4y = 6

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Question 144044: solve using the substitution method
y = 3 - x
2x + 4y = 6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x%2B4y=6
y=3-x



2x%2B4%283-x%29=6 Plug in y=3-x into the first equation. In other words, replace each y with 3-x. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


2x%2B12-4x=6 Distribute


-2x%2B12=6 Combine like terms on the left side


-2x=6-12Subtract 12 from both sides


-2x=-6 Combine like terms on the right side


x=%28-6%29%2F%28-2%29 Divide both sides by -2 to isolate x



x=3 Divide




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



y=3-%283%29 Substitute 3 for each x


y=0 Simplify


So our answer is x=3 and y=0 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+%286-2x%29%2F4%2C+3-x%29+ Graph of 2x%2B4y=6 (red) and y=3-x (green)