SOLUTION: Y-2x=-2 and x^2+y^2+2x-3y=19. Please solve it algebraically

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Question 856657: Y-2x=-2 and x^2+y^2+2x-3y=19. Please solve it algebraically
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The intersection of a line and a circle.
y-2x=-2
y=2x-2
Substitute,
x%5E2%2By%5E2%2B2x-3y=19
x%5E2%2B%282x-2%29%5E2%2B2x-3%282x-2%29=19
x%5E2%2B%284x%5E2-8x%2B4%29%2B2x-%286x-6%29=19
5x%5E2-12x%2B10=19
5x%5E2-12x-9=0
%285x%2B3%29%28x-3%29=0
Two solutions:
5x%2B3=0
5x=-3
x=-3%2F5
Then
y=2%28-3%2F5%29-2
y=-6%2F5-10%2F5
y=-16%2F5
and
x-3=0
x=3
Then
y=2%283%29-2
y=6-2
y=4
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(-3/5,-16/5) and (3,4)
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