Question

1. how many solutions does the system have and what does the graph look like? $-4x + y = 3$ and $-8x + 2y = -6$

a. no solution
b. one solution
c. infinite solutions
d. parallel lines
e. intersecting lines
f. single line

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(-4x + y=3\), we can rewrite it as \(y = 4x+3\). The slope \(m_1\) of this line is \(4\) and the y - intercept \(b_1\) is \(3\).

For the second equation \(-8x + 2y=-6\), we divide the entire equation by \(2\) to simplify. We get \(-4x + y=-3\), and then rewrite it as \(y = 4x - 3\). The slope \(m_2\) of this line is \(4\) and the y - intercept \(b_2\) is \(-3\).

Step2: Analyze the slopes and y - intercepts

Since the slopes of the two lines \(m_1=m_2 = 4\) (the lines are parallel) and the y - intercepts \(b_1
eq b_2\) ( \(3
eq - 3\) ), the two lines are parallel and will never intersect. So the system of equations has no solution.

Answer:

A. No Solution, D. Parallel Lines