SOLUTION: y=x+2 2x+y=11 Could someone please help me?

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Question 120606: y=x+2
2x+y=11
Could someone please help me?
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
2x%2By=11
y=x%2B2



2x%2Bx%2B2=11 Plug in y=x%2B2 into the first equation. In other words, replace each y with x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.




3x%2B2=11 Combine like terms on the left side


3x=11-2Subtract 2 from both sides


3x=9 Combine like terms on the right side


x=%289%29%2F%283%29 Divide both sides by 3 to isolate x



x=3 Divide




Now that we know that x=3, we can plug this into y=x%2B2 to find y



y=%283%29%2B2 Substitute 3 for each x


y=5 Simplify


So our answer is x=3 and y=5 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+-7%2C+7%2C+-7%2C+7%2C+11-2x%2C+x%2B2%29+ Graph of 2x%2B1y=11 (red) and y=x%2B2 (green)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system of equations:
1) y+=+x%2B2
2) 2x%2By+=+11
You can use the substitution method. Substitute the y+=+x%2B2 from equation 1) into equation 2) and solve for x.
2x%2B%28x%2B2%29+=+11 Simplify.
3x%2B2+=+11 Subtract 2 from both sides.
3x+=+9 Divide both sides by 3.
x+=+3 Now substitute this value of x into either of the two original equations and solve for y. Let's use equation 1)
y+=+x%2B2 Substitute x+=+3
y+=+3%2B2
y+=+5
The solution is: (3, 5) and this is the point of intersection of the two lines represented by the two equations.
graph%28600%2C400%2C-5%2C5%2C-5%2C7%2Cx%2B2%2C-2x%2B11%29