SOLUTION: Please assist me in comprehending how to solve this problem. Find the solution of the system y = x^2 + 5 and y = 2x + 4

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Question 6394: Please assist me in comprehending how to solve this problem.
Find the solution of the system y = x^2 + 5 and y = 2x + 4
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
y = x^2 + 5
y = 2x + 4
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Therefore,
x^2 + 5 = 2x + 4
x^2 - 2x + 5 - 4 = 0
x^2 - 2x + 1 = 0


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-2%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-2x%2B1+=+1%28x-1%29%2A%28x-1%29

Again, the answer is: 1, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B1+%29



Therefore,x=1
then y=2x+4=2+4=6


x=1,y=6

Hope this helps,
good luck