Practice Linear System Behavior in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

How the solutions of a linear system relate to the geometric arrangement of the lines.

Two lines can cross (one solution), be parallel (no solution), or overlap (infinite solutions).

Example 1

easy
Classify the system: \begin{cases} 2x + y = 5 \\ 4x + 2y = 10 \end{cases}

Example 2

medium
Classify: \begin{cases} x - 3y = 2 \\ 2x - 6y = 7 \end{cases}

Example 3

easy
Does \begin{cases} x + y = 3 \\ x - y = 1 \end{cases} have one solution, no solution, or infinitely many?

Example 4

medium
Classify: \begin{cases} 3x - y = 4 \\ 6x - 2y = 8 \end{cases}