Question

graph these equations:
$y = \frac{1}{2}x - 4$
$y = \frac{1}{2}x - 4$
click to select points on the graph.
graph with coordinate plane
$y = \frac{1}{2}x - 4$ (green) $y = \frac{1}{2}x - 4$ (blue)
how many solutions does the system of equations have?
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the equations

The system has two equations: \( y = \frac{1}{2}x - 4 \) and \( y = \frac{1}{2}x - 4 \). They are identical.

Step2: Determine the number of solutions

For a system of linear equations, if the two equations represent the same line (identical equations), then every point on the line is a solution. So, there are infinitely many solutions.

Answer:

infinitely many solutions