Question

What are the solutions to the following system?
-2 x² + y = -5
y=-3x²+5

Answer 1

`x=\pm√(2)`

Explanation:

This system of equations is convenient, because the second equation already expresses y in terms of x. Now, you can substitute that in.

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

Multiplying both sides by -1 and bringing the 5 over:

`2x^2+3x^2-10=0`

Combining like terms and factoring out 5:

`5(x^2-2)=0`

Factoring:

`5(x-√(2))(x+√(2))=0`

Solutions:
`x=\pm√(2)`

Hope this helps!