Currently in a pre-calculus class and of course having trouble.

Question

So question came up I prefer using elimination however I was asked that You cannot use elimination for this system/problem Why?

x+y=3

x²+y²=25

I believe you use substitution but I'm not tracking why I can't use elimination and having issues solving.

Answer 1

x^2 +y^2 = 25

x+y = 3

x^2 +2xy + y^2 = 9

x^2 +y^2 = 25

2xy = 9-25 =-16

XY = -8

graph the circle and line and find the two intersection points

looks like about (-7/4, 19/4) and (19/4, -7/4)

19/4 times -7/4 = -19(7)/16 = about -8.3 = about -8

so that's a close approximation to (x,y) intersection points