SOLUTION: What is the solution to the sysytem of equations y=2x and y=-x+3? Thank You for your time!!

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Question 127303: What is the solution to the sysytem of equations y=2x and y=-x+3?
Thank You for your time!!
Found 3 solutions by jim_thompson5910, checkley71, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
y=2x
y=-x%2B3



-x%2B3=2x Plug in y=-x%2B3 into the first equation. In other words, replace each y with -x%2B3. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


-x%2B3=2x Distribute



-x=2x-3Subtract 3 from both sides


-x-2x=-3 Subtract 2x from both sides


-3x=-3 Combine like terms on the left side


x=%28-3%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=1 Divide




Now that we know that x=1, we can plug this into y=-x%2B3 to find y



y=-%281%29%2B3 Substitute 1 for each x


y=2 Simplify


So our answer is x=1 and y=2 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+2x%2C+-x%2B3%29+ Graph of y=2x (red) and y=-x%2B3 (green)

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x & y=-x+3 .
because these 2 equations are both equal to y then we can combine them thus:
2x=-x+3
2x+x=3
3x=3
x=3/3
x=1 answer.
y=2*1=2 answeer
y=-1+3=2 answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What is the solution to the sysytem of equations y=2x and y=-x+3?
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Substitute to get:
2x = -x+3
3x = 3
x = 1
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Substitute to solve for "y":
y = 2*1 = 2
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Cheers,
Stan H.