Linear System Behavior Math Example 4

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

Example 4

medium
Classify: {3x−y=46x−2y=8\begin{cases} 3x - y = 4 \\ 6x - 2y = 8 \end{cases}

Solution

  1. 1
    36=−1−2=48=12\frac{3}{6} = \frac{-1}{-2} = \frac{4}{8} = \frac{1}{2}. All ratios equal.
  2. 2
    Dependent — infinitely many solutions (same line).

Answer

Dependent (infinitely many solutions)
The second equation is exactly twice the first, so they represent the same line. Any point on 3x−y=43x - y = 4 is a solution.

About Linear System Behavior

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).

Learn more about Linear System Behavior →

More Linear System Behavior Examples

Example 1 easy

Classify the system: [formula]

Example 2 medium

Classify: [formula]

Example 3 easy

Does [formula] have one solution, no solution, or infinitely many?

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