Question

10b. (1 pt.) which of the is the correct graph of the given system?
$y < 2x -1$ and $y > \frac{2}{3}x +4$

Explanation:

Step1: Identify line styles

Both inequalities use $<$ and $>$, so both lines $y=2x-1$ and $y=\frac{2}{3}x+4$ are dashed.

Step2: Test shading for $y<2x-1$

Pick a test point, e.g., $(0,0)$: $0 < 2(0)-1$ → $0 < -1$ is false. Shade the region below $y=2x-1$.

Step3: Test shading for $y>\frac{2}{3}x+4$

Use $(0,0)$: $0 > \frac{2}{3}(0)+4$ → $0 > 4$ is false. Shade the region above $y=\frac{2}{3}x+4$.

Step4: Find overlapping region

The solution is the intersection of the two shaded regions, which is the small area bounded above by $y=\frac{2}{3}x+4$ and below by $y=2x-1$, with both lines dashed. This matches the top-left graph.

Answer:

The correct graph is the top-left option (the graph with a small white triangular region bounded by two dashed lines, with shading outside this triangle in the upper and lower areas).