SOLUTION: Solve x^2 + y^2 = 5 x - 3y = 5

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Question 65846This question is from textbook An Incremental Development
: Solve
x^2 + y^2 = 5
x - 3y = 5 This question is from textbook An Incremental Development

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
E1) x^2 + y^2 = 5
E2) x - 3y = 5 ~~> x=3y+5
Substititute 3y+5 in for x in E1.
%283y%2B5%29%5E2%2By%5E2=5
9y%5E2%2B30y%2B25%2By%5E2=5
10y%5E2%2B30y%2B25=5
10y%5E2%2B30y%2B25-5=5-5
10y%5E2%2B30y%2B20=0
10%28y%5E2%2B3y%2B2%29=0
10%28y%5E2%2B3y%2B2%29%2F10=0%2F10
y%5E2%2B3y%2B2=0
%28y%2B2%29%28y%2B1%29=0
y+2=0 or y+1=0
y=-2 or y=-1
Substitute these values in for y in E2 and solve for x:
x=3(-2)+5 or x=3(-1)+5
x=-6+5 or x=-3+5
x=-1 or x=2
The circle (E1) is intercected by the line (E2) in two places:
(-1,-2) and (2,-1)
Graphically,

Happy Calculating!!!