SOLUTION: Solve the nonlinear system by substitution: {{{x^2+y^2=10 -3X+Y=0}}}

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I assume it looks like this right?




Solve the 2nd equation for y

Plug in y=3x

Square 3x to get

Subtract 10 from both sides


Combine like terms

Factor out 10

Set each factor equal to zero

Add one to both sides

Take the square root of both sides


So the solution breaks down to:

or







Now plug in x=1 to find y



So when x=1, y=3


Now plug in x=-1 to find y



So when x=-1, y=-3



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Answer:
So our solutions are

and which makes the point (1,3)


and


and which makes the point (-1, -3)