Practice Linear System Behavior in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The classification of a system of linear equations based on the geometric relationship of the lines: intersecting at one point (one unique solution), parallel with no intersection (no solution), or coincident/overlapping (infinitely many solutions).
Two lines can cross (one solution), be parallel (no solution), or overlap (infinite solutions).
Example 1
easyClassify the system: \begin{cases} 2x + y = 5 \\ 4x + 2y = 10 \end{cases}
Example 2
mediumClassify: \begin{cases} x - 3y = 2 \\ 2x - 6y = 7 \end{cases}
Example 3
easyDoes \begin{cases} x + y = 3 \\ x - y = 1 \end{cases} have one solution, no solution, or infinitely many?
Example 4
mediumClassify: \begin{cases} 3x - y = 4 \\ 6x - 2y = 8 \end{cases}