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

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)   (Show Source): You can put this solution on YOUR website!
Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Subtract 3 from both sides

Subtract 2x from both sides

Combine like terms on the left side

Divide both sides by -3 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and 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 of (red) and (green)

Answer by checkley71(8403)   (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)   (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?
--------------
Substitute to get:
2x = -x+3
3x = 3
x = 1
--------
Substitute to solve for "y":
y = 2*1 = 2
-----------
Cheers,
Stan H.
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