Consistency Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is {3xโˆ’y=7x+2y=1\begin{cases} 3x - y = 7 \\ x + 2y = 1 \end{cases} consistent?

Solution

  1. 1
    The ratios 31โ‰ โˆ’12\frac{3}{1} \neq \frac{-1}{2}, so the lines intersect.
  2. 2
    Yes, consistent (has a unique solution).

Answer

Yes, consistent.
Non-parallel lines always intersect, guaranteeing at least one solution. A system with a unique solution is both consistent and independent.

About Consistency

A system of equations is consistent when there exists at least one set of variable values that satisfies every equation simultaneously.

Learn more about Consistency โ†’

More Consistency Examples

Example 1 easy

Is the system [formula] consistent?

Example 2 medium

For what value of [formula] is [formula] consistent?

Example 4 medium

Is [formula] consistent?

โ† All Consistency Examples Consistency Concept