Identifying Systems with No Solution or Infinitely Many Solutions

Question:
Graph the following system of equations and determine the number of solutions. Explain whether the system has no solution, one solution, or infinitely many solutions. Equation 1: 3x minus 2y equals 8. Equation 2: 6x minus 4y equals 20.

Identifying Systems with No Solution or Infinitely Many Solutions

This lesson explores how to determine the number of solutions in a linear system by rewriting equations in slope-intercept form and comparing slopes and y-intercepts. Students learn that parallel lines — same slope, different intercepts — produce an inconsistent system with no solution, confirmed both graphically and algebraically.

In this lesson, you will learn to:
• Rewrite linear equations in slope-intercept form by solving for y
• Identify parallel lines by comparing slopes and y-intercepts
• Determine that a system with parallel lines has no solution (inconsistent system)
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