Question

Solve system by using elimination.
y=-3x^2-30x-76
y=2x^2+20x+44

Answer 1

`x_(1)=-4`

`x_(2)=-6`

`y=-4`

Explanation:

We have the following equations:

`y=-3x^(2)-30x-76` (1)

`y=2x^2+20x+44` (2)

Multiplying (1) by
`2` and (2) by
`3`:

`2y=-6x^(2)-60x-152` (3)

`3y=6x^2+60x+132` (4)

Summing (3) and (4):

`5y=-20` (5)

Isolating
`y`:

`y=-4` (6)

Substituting (6) in (2):

`-4=2x^2+20x+44` (7)

Rearranging the equation:

`0=x^2+10x+24` (8)

Solving with the quadratic formula
`x=\frac{-b\pm\sqrt{b^(2)-4ac}}{2a}`, where
`a=1`,
`b=10`,
`c=24`, in order to find the two values of
`x` that satisfy the system of equations:

`x=\frac{-10\pm\sqrt{10^(2)-4(1)(24)}}{2(1)}` (9)

`x_(1)=-4` (10)

`x_(2)=-6` (11)