Question

which ordered pair is in the solution set of the system of linear inequalities?
$y > \frac{3}{2}x - 1$
$y < \frac{3}{2}x - 1$
\\(\circ\\) $(-5, 2)$
\\(\circ\\) $(2, 2)$
\\(\circ\\) $(5, 2)$
\\(\circ\\) no solution

Explanation:

Step1: Analyze inequality logic

A number cannot be both greater than and less than the same value simultaneously. For any ordered pair $(x,y)$, $y$ cannot satisfy both $y > \frac{3}{2}x - 1$ and $y < \frac{3}{2}x - 1$.

Step2: Verify with graph

The shaded regions for $y > \frac{3}{2}x - 1$ (blue) and $y < \frac{3}{2}x - 1$ (red) do not overlap, meaning there is no shared area of solutions.

Answer:

no solution