Practice Consistency in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A system of equations is consistent when there exists at least one set of variable values that satisfies every equation simultaneously.
The constraints don't contradict each other—there's some answer that works.
Example 1
easyIs the system \begin{cases} x + y = 5 \\ 2x + 2y = 8 \end{cases} consistent?
Example 2
mediumFor what value of k is \begin{cases} x + 2y = 3 \\ 2x + 4y = k \end{cases} consistent?
Example 3
easyIs \begin{cases} 3x - y = 7 \\ x + 2y = 1 \end{cases} consistent?
Example 4
mediumIs \begin{cases} x + y + z = 1 \\ x + y + z = 3 \end{cases} consistent?