Question

the graph represents a system of linear equations. determine the number of solutions of the system. one solution no solution infinitely many solutions

Explanation:

Step1: Analyze the graph

The graph shows a single line (since there's only one blue line visible, implying the two linear equations in the system are actually the same line, or coinciding lines).

Step2: Relate to solution types

For a system of linear equations, if the lines are coinciding (same line), they have infinitely many solutions (every point on the line is a solution). If they are parallel, no solution; if they intersect at one point, one solution. Here, since it's one line (coinciding), the system has infinitely many solutions. Wait, but wait—wait, maybe I misread. Wait, the problem says "the graph represents a system of linear equations"—but in the image, is there one line or two? Wait, looking at the graph, maybe it's two lines that are coinciding (same line). So when two lines are the same (coinciding), the system has infinitely many solutions. But wait, the options are "one solution", "no solution", "infinitely many solutions". Wait, maybe I made a mistake. Wait, no—if the graph shows only one line, that means the two equations are dependent (same line), so infinitely many solutions. But let me check again. Wait, maybe the graph is of two lines that are coincident (overlapping), so they have infinitely many solutions. So the correct option is "infinitely many solutions". Wait, but let's confirm:

• One solution: lines intersect at one point.
• No solution: lines are parallel (no intersection).
• Infinitely many: lines are coincident (same line, all points intersect).

Since the graph here shows a single line (so the two equations in the system are the same line), the system has infinitely many solutions.

Answer:

infinitely many solutions