SOLUTION: x^2 + y^2 =25 and 2x -3y =-6 i need to find all real solutions of the nonlinear system of equations

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Question 737787: x^2 + y^2 =25 and 2x -3y =-6 i need to find all real solutions of the nonlinear system of equations
Answer by Susan-math(40) About Me  (Show Source):
You can put this solution on YOUR website!
2x-3y=-6 gives x=%283%2F2%29y-3
so }}}x^2+y^2=25}}} becomes %28%283%2F2%29y-3%29%5E2%2By%5E2=25
so %289%2F4%29y%5E2-9y%2B9+%2By%5E2=25
and %2813%2F4%29y%5E2-9y-16=0
Using the quadratic formula with a=13/4, b=-9 c=-16
Then (((y=(9 +-sqrt(81-4(13/4)(-16)))/2(13/4)=(9+-sqrt(289))/(13/2)=(9+-17)/(13/2)}}} which gives y=4 or y=-16/13
substitute those into the linear equation to find x.
y=4 gives x=%283%2F2%29%284%29-3=6-3=3
y=-16/13 gives x=%283%2F2%29%28-16%2F13%29-3=-24%2F13-3=-%2863%2F13%29