Question

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Explanation:

Step1: Recall Linear Equation Solution

A system of two linear equations has a solution where their graphs intersect. For no solution, lines must be parallel (same slope, different y - intercepts).

Step2: Sketch Parallel Lines

Draw two distinct straight lines with the same slope (e.g., \(y = 2x+1\) and \(y = 2x + 3\)). These lines never meet.

Step3: Explain the Graph

Parallel lines have the same slope, so they never intersect. Since a solution to the system is a point \((x,y)\) that satisfies both equations (lies on both lines), no intersection means no common point, hence no solution.

Answer:

To show a system of two linear equations with no solution, sketch two parallel lines (e.g., \(y = 2x + 1\) and \(y=2x + 3\)). Parallel lines have the same slope and different y - intercepts, so they never intersect. A solution to the system is a point that lies on both lines; since the lines never meet, there is no such point, so the system has no solution.