Question

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

Answer 1

Answer:

$x=\pm\sqrt{2}$

Step-by-step 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:

$5(x-\sqrt{2})(x+\sqrt{2})=0$

Solutions: $x=\pm\sqrt{2}$

Hope this helps!