Question

1.What are the solutions to the following system?

-2x^2+y=-5
y=-3x^2+5

A) (0,2)
B) (1,-2)
C) (sq. root of 2,-1) and (- sq. root of 2,-1)
D) (sq. root of 5, -10) and (-sq. root of 5,-10)

Answer 1

-2x²+y=-5 ==> y=2x²-5
y=-3x²+5 ==> y=-3x²+5

since y=y then 2x²-5 = -3x²+5===> 5x²=10 x²=2 & x₁=√2 & x₂= - √2
Plug √2 into x (of 2x²-5) ==>y = f(√2) = -1 & y= f(-√2) = -1
So the Solution (√2, -1)
& If you plug √2 into x (-3x²+5) => y= f(√2) = -1
So in both cases x=√2 & y=-1

Answer 2

answer: C. (√2, -1) and (√2, -1).