Question

which graph shows a system with an infinite number of solutions?
graph a
graph b
graph c
text description for graph
a. graph a
b. graph c
c. graph b

Explanation:

Step1: Recall solution conditions

A system of linear equations has infinite solutions when the equations are equivalent (same line). So, we need to check if the two lines in each graph represent the same equation.

Step2: Analyze Graph A

The two lines have different slopes (since they are not parallel and not the same line), so they intersect at one point (one solution).

Step3: Analyze Graph B

The two lines have the same slope ($-\frac{3}{2}$) but different y - intercepts (5 and - 3), so they are parallel (no solution).

Step4: Analyze Graph C

Simplify the second equation: $2y = 4x - 2$ divides both sides by 2, we get $y=2x - 1$, which is the same as the first equation $y = 2x-1$. So the two lines are the same, meaning infinite solutions.

Answer:

B. Graph C