SOLUTION: What is the points of intersection of these equations y=x+3 x^2+y^2+4x-8y+11

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Question 257977: What is the points of intersection of these equations
y=x+3
x^2+y^2+4x-8y+11
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

system%28y=x%2B3%2C+x%5E2%2By%5E2%2B4x-8y%2B11=0%29

Substitute %28x%2B3%29 for y in the second equation:

x%5E2%2By%5E2%2B4x-8y%2B11=0

x%5E2%2B%28x%2B3%29%5E2%2B4x-8%28x%2B3%29%2B11=0

x%5E2%2B%28x%2B3%29%28x%2B3%29%2B4x-8x-24%2B11=0

x%5E2%2B%28x%5E2%2B3x%2B3x%2B9%29%2B4x-8x-24%2B11=0

x%5E2%2B%28x%5E2%2B6x%2B9%29%2B4x-8x-24%2B11=0

x%5E2%2Bx%5E2%2B6x%2B9%2B4x-8x-24%2B11=0

2x%5E2%2B2x-4=0

Divide every term by 2

x%5E2%2Bx-2=0

Factor:

%28x%2B2%29%28x-1%29=0

Use zero-factor principle:

x%2B2=0 gives solution x=-2

x-1=0 gives solution x=1

Now we must find the value of y for each of these
two values for x.

For x=-2 we substitute -2 for x in 

y=x%2B3

y=%28-2%29%2B3

y=1

So one solution is (x,y) = (-2,1)

For x=1 we substitute 1 for x in 

y=x%2B3

y=%281%29%2B3

y=4

So the other solution is (x,y) = (1,4)

Graphically we have this



Edwin