SOLUTION: How do you get the answer to 2x+7y=3 x=1-4y

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Question 126070This question is from textbook algebra 1
: How do you get the answer to 2x+7y=3
x=1-4y This question is from textbook algebra 1

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x%2B7y=3
x=1-4y



2%281-4y%29%2B7y=3 Plug in x=1-4y into the first equation. In other words, replace each x with 1-4y. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


2-8y%2B7y=3 Distribute


-y%2B2=3 Combine like terms on the left side


-y=3-2Subtract 2 from both sides


-y=1 Combine like terms on the right side


y=%281%29%2F%28-1%29 Divide both sides by -1 to isolate y



y=-1 Divide




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



x=1-4%28-1%29 Substitute -1 for each y


x=5 Simplify


So our answer is x=5 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+-4%2C+6%2C+-4%2C+6%2C+%283-2x%29%2F7%2C+%28x-1%29%2F%28-4%29%29+ Graph of 2x%2B7y=3 (red) and x=1-4y (green)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2x+7y=3
x=1-4y
----------------
Substitute to solve for "y":
2(1-4y) + 7y = 3
2-8y + 7y = 3
-y = 1
y = -1
----------------
Substitute to solve for "x"
x = 1-4*-1
x = 5
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Cheers,
Stan H.