SOLUTION: how do you solve this system of equations x squared + y squared = 9 5x-y=-3

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Question 53333This question is from textbook
: how do you solve this system of equations
x squared + y squared = 9
5x-y=-3 This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Geometrically:The first equation is a circle centered at the origin and a radius of three. The second one is a line. If you think about it a line can miss a circle and get no solution. It can barely touch a circle and get only one solution. Or it can go right through a circle, and have two solutions.
Algebraically, we can find out the solution by solving the second equation for y and substituting it into the first equation. Then we can solve for x. The solution we get for x can then be substituted into the second equation and solve for y.
x%5E2%2By%5E2=9
5x-y=-3
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5x-y=-3
-5x%2B5x-y=-5x-3
-y=-5x-3
-y%2F-1=-5x%2F-1-3%2F-1
y=5x%2B3
Substitute that value in for y in the first equation and solve for x:
x%5E2%2B%285x%2B3%29%5E2=9
x%5E2%2B%285x%2B3%29%285x%2B3%29=9
x%5E2%2B25x%5E2%2B15x%2B15x%2B9=9
%281%2B25%29x%5E2%2B%2815%2B15%29x%2B9=9
26x%5E2%2B30x%2B9=9
26x%5E2%2B30x%2B9-9=9-9
26x%5E2%2B30x=0
2x%2813x%2B15%29=0
2x=0
2x/2=0/2
x=0
and
13x+15=0
13x+15-15=0-15
13x=-15
13x/13=-15/13
x=-15/13
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Substitute x=0 into the second equation and you get:
5(0)-y=-3
-y=-3
-y/-1=-3/-1
y=3
(0,3) is one solution.
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Substitute x=-15/13 into the second equation and you get:
5(-15/13)-y=-3
-75/13-y=-3
+75/13-75/13-y=-3+75/13
-y=-39/13+75/13
-y=-36/13
(-15/13,-36/13) is the second solution.
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Graphically we have: