Question

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

Answer 1

Answer:

(x1,y1) = (-2,-2)

(x2,y2) = (-4,-2)

Step-by-step explanation:

$y=-x^{2} -6x-10\\y=3x^{2} +18x+22$

Move Variables To The Left Side and Change Their Signs

$y+x^{2}+6x=-10\\ y-3x^{2}-18x=22$

Multiply Both Sides Of The Equation By -1

$y+x^{2} +6x=-10\\-y+3x^{2} +18x=-22$

Sum The Equations Vertically To Eliminate At Least One Variable

$4x^{2} +24x=-32$

Solve The Equation For X

$x=-2\\x=-4$

Substitute The Given Value of X Into The Equation

$y-3*(-2)^{2} -18*(-2)=22\\y-3*(-4)^{2} -18*(-4)=22$

Solve The Equation For Y

$y=-2\\y=-2$

Answer 2

Answer:

(-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).