How many solutions are there for the system shown below?
x^2+y^2=25
x-y^2=-5

1
2
3
4

Question

How many solutions are there for the system shown below?
x^2+y^2=25
x-y^2=-5

1
2
3
4

btaylor · Answer

graph them, then count the intersection points.

ganeshie8 · Answer

second curve starts from -5 right... so 3 intersections

btaylor · Answer

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anonymous · Answer

Thanks, :)

anonymous · Answer

or if you want you could use the elimination method so by the 2 questions you gave (1)x^2+y^2=25 and (2)x-y^2=-5  from (1) lets solve for y^2 so we could put it into (2)

so from (1) we got y^2 = 25 - x^2 now lets plug this into (2) to get x - (25-x^2) = -5 --> x-25+x^2= -5 and now lets put everything into one side to get x^2 + x - 20 = 0 and this is a quadratic formula and when we factor this out

we get (x+5)(x-4)=0 so therefore when x=-5 and when x=4 and therefore when x=-5 y=0 and of when x=4 y=3 and when x=4 y=-3 since we took the square root of 9

so hence we got 3 solutions