Question

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

Explanation:

Step1: Recall solution types for linear systems

A system of linear equations has:

• No solution: Lines are parallel (same slope, different y - intercepts).
• One solution: Lines intersect at one point (different slopes).
• Infinitely many solutions: Lines are coincident (same slope, same y - intercept).

Step2: Analyze the graph

The two lines in the graph intersect at exactly one point. This means the system has one solution (since intersecting lines with different slopes have a single common point, which is the solution).

Answer:

one solution