Question

33. Solve with elimination. y = – 3x2 – 30x – 76
y = 2x2 + 20x + 44

Answer 1

(-4, -4) and (-6, -4)

Explanation:

Subtract the first equation from the second to eliminate y.

(y) -(y) = (2x^2 +20x +44) -(-3x^2 -30x -76)

0 = 5x^2 +50x +120

0 = x^2 +10x +24

0 = (x +4)(x +6)

Solutions are values of x that make the factors zero:

x = -4, x = -6

The corresponding y-values are found by putting these values of x into either polynomial equation.

y = 2((x +10)x +22) . . . . . rearrange the second equation to Horner form

y = 2((-4 +10)(-4) +22) = 2(6(-4) +22) = -4 . . . . for x = -4

y = 2((-6 +10)(-6) +22) = 2(4(-6) +22) = -4 . . . . for x = -6

The solutions are (-4, -4) and (-6, -4).