Question

question 2 (multiple choice worth 6 points) (06.03r mc)
solve the system of equations.
$8x - y = 8$
$8x^2 - y = 8$
(0, 8) and (0, -8)
(1, 0) and (0, -8)
(2, 8) and (1, 0)
(3, 16) and (2, 24)

Explanation:

Step1: Isolate $y$ from linear eq.

From $8x - y = 8$, rearrange to get $y = 8x - 8$.

Step2: Substitute $y$ into quadratic eq.

Substitute $y=8x-8$ into $8x^2 - y = 8$:
$$8x^2 - (8x - 8) = 8$$
Simplify:
$$8x^2 -8x +8 =8$$
$$8x^2 -8x =0$$

Step3: Factor and solve for $x$

Factor out $8x$:
$$8x(x - 1) = 0$$
Set each factor to 0:
$8x=0 \implies x=0$; $x-1=0 \implies x=1$

Step4: Find corresponding $y$ values

For $x=0$: $y=8(0)-8=-8$
For $x=1$: $y=8(1)-8=0$

Answer:

(1, 0) and (0, -8)