Solve equations with elimination method, ! y=-x^2-6x-10 y=3x^2+18x+22

(-4,-2) and (-2, -2)

Step-by-step explanation:

Eliminate y by equating the two given equations:

y=-x^2-6x-10

y = 3x^2 + 18x + 22 = -x^2 - 6x - 10.

Next, combine like terms, obtaining:  4x^2 + 24x + 32 = 0

Simplify by dividing all terms by 4:  x^2 + 6x + 8 = 0.

Factor:   x^2 + 6x + 8 = 0 => (x + 4)(x + 2) = 0.

Solve for x:  x = -4 and x = -2.

Find the y-values associated with these x-values:

y = -(-4)^2 - 6(-4) - 10 = -16 + 24 - 10 = -2, so that one solution is (-4,-2)

y = -(-2)^2 - 6(-2) - 10 = -4 + 12 - 10 = -2, so that the other sol'n is (-2, -2).