Question

solve the system of equations.
y = 6x
y = x² + 5
a. (-1, -6) and (5, 30)
b. (1, 6) and (5, 30)
c. (1, 6) and (3, 18)
d. (-3, -18) and (-1, -6)

Explanation:

Step1: Set equations equal

$6x = x^2 + 5$

Step2: Rearrange into quadratic

$x^2 - 6x + 5 = 0$

Step3: Factor quadratic

$(x-1)(x-5) = 0$

Step4: Find x-values

$x=1$ or $x=5$

Step5: Find y-values

For $x=1$: $y=6(1)=6$; For $x=5$: $y=6(5)=30$

Answer:

B. (1, 6) and (5, 30)