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).
Showing a random 20 of 50 problems.
Example 1
easyHow many solutions can a system of two linear equations in two unknowns have?
Example 2
easyA consistent and independent system has __________ solution(s).
Example 3
mediumFor what does have infinitely many solutions?
Example 4
easyLines and : classify.
Example 5
easyGraphically, two lines coincide (lie on top of each other). The system is __________.
Example 6
hardFor what values of does have a UNIQUE solution?
Example 7
easyTwo lines have the same slope but different -intercepts. How many solutions does the system have?
Example 8
mediumClassify:
Example 9
hardFor what does have NO unique solution?
Example 10
easyLines and : same slope or different?
Example 11
mediumFor what does have infinitely many solutions?
Example 12
mediumFor what value of does have infinitely many solutions?
Example 13
mediumClassify: .
Example 14
easyAfter elimination, a system reduces to . How many solutions?
Example 15
mediumClassify:
Example 16
easyLines and : classify.
Example 17
easyClassify by graph: two lines drawn lie on top of each other. Solution count?
Example 18
mediumClassify: .
Example 19
challengeFind all for which has a UNIQUE solution.
Example 20
mediumClassify: .