Answer:
Given system of inequalities:
[tex]\large\begin{cases}y < \frac{2}{3}x\\y\geq-x+2\end{cases}[/tex]
When graphing inequalities:
- < or > = dashed line
- ≤ or ≥ = solid line
- < or ≤ = shade below the line
- > or ≥ = shade above the line
[tex]y < \dfrac{2}{3}x[/tex]
The slope of the first inequality is 2/3, therefore at x = 1, y = 2/3.
So the correct line for the first inequality is the dotted line with the shallower slope.
As the relation is < for this inequality, the shading should be below the dotted line.
[tex]y\geq-x+2[/tex]
From inspection of the given graphs, the line of the second inequality (solid line) is the same in all graphs.
As the relation is ≥ for this inequality, the shading should be above the solid line.
Therefore, the only graph that satisfies these conclusions is graph D (attached).
