Question

Please solve equations with elimination method, please!

y=-x^2-6x-10

y=3x^2+18x+22

Answer 1

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

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

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

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

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).