Question

1. which of the following pairs satisfy the system $y = 4x + 2$ and $y = 4x - 1$?

a. none of the available answers
b. $(0,2)$
c. $(2,10)$
d. $(1,6)$

Explanation:

Step1: Analyze the system's slopes

Both lines have slope $m=4$, so they are parallel.

Step2: Check y-intercepts

First line: $y=4x+2$, y-intercept $(0,2)$.
Second line: $y=4x-1$, y-intercept $(0,-1)$.

Step3: Determine solution existence

Parallel lines with different y-intercepts never intersect, so there is no solution pair.

Step4: Verify given options

• For (0,2): $y=4(0)-1=-1

eq2$, fails second equation.

• For (2,10): $y=4(2)-1=7

eq10$, fails second equation.

• For (1,6): $y=4(1)-1=3

eq6$, fails second equation.

Answer:

a. None of the available answers