Question

x = 8
y = x^2 + 8
the graphs of the equations in the given system of equations intersect at the point (x, y) in the xy - plane. what is the value of y?
a) 8
b) 24
c) 64
d) 72

Explanation:

Step1: Identify x from the first equation

The first equation is \( x = 8 \). So the x - coordinate of the intersection point is 8.

Step2: Substitute x into the second equation

We have the second equation \( y=x^{2}+8 \). Substitute \( x = 8 \) into this equation. Then \( y=(8)^{2}+8 \).

Step3: Calculate the value of y

First, calculate \( 8^{2}=64 \). Then \( y = 64 + 8=72 \)? Wait, no, wait. Wait, \( 8^2=64 \), \( 64 + 8 = 72 \)? But wait, let's check again. Wait, maybe I made a mistake. Wait, the second equation: if \( x = 8 \), then \( y=8^{2}+8=64 + 8 = 72 \)? But the options are A)8, B)24, C)64, D)72. Wait, but let's re - examine the problem. Wait, maybe the second equation is \( y=x^{2}+8 \)? Wait, no, maybe the second equation is \( y = x^{2}+8 \)? Wait, if \( x = 8 \), then \( y=8^2 + 8=64 + 8 = 72 \). But let's check the options. Option D is 72. But wait, maybe I misread the equation. Wait, maybe the second equation is \( y=x^{2}+8 \)? Wait, let's do the calculation again. \( 8\times8 = 64 \), \( 64+8 = 72 \). So y is 72.

Answer:

D)72