Question

$y = -\frac{3}{2}x + 4$
$y = -\frac{1}{4}x - 1$
which describes the system of equations above?
consistent and dependent
consistent and independent
inconsistent

Explanation:

Step1: Compare slopes of equations

The slopes are $-\frac{3}{2}$ and $-\frac{1}{4}$; they are not equal.

Step2: Analyze system type

Unequal slopes mean lines intersect at one point, so the system has exactly one solution. A system with at least one solution is consistent, and independent if it has exactly one unique solution.

Answer:

consistent and independent