SOLUTION: Solve the following system of equations algebraically: y = x^2-6x+6 y-x= -4

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Question 159055: Solve the following system of equations algebraically:
y = x^2-6x+6
y-x= -4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.y+=+x%5E2-6x%2B6
2.y-x=-4
Use eq. 2 and find an expression for y in terms of x.
2.y-x=-4
y=x-4
Substitute into eq. 1 and solve for x.
1.y+=+x%5E2-6x%2B6
x-4+=+x%5E2-6x%2B6
x%5E2-7x%2B10=0
%28x-5%29%28x-2%29=0
Two solutions, first find x, then corresponding y.
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.
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%28x-5%29=0
x=5
From eq. 2,
y=x-4
y=5-4
y=1
First solution : x=5, y=1
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%28x-2%29=0
x=2
from eq. 2,
y=x-4
y=2-4
y=-2
Second solution : x=2, y=-2
Check the solutions graphically by plotting both curves,