Given:
[tex]\begin{gathered} y\text{ }\leq\text{ 2x + (-4)} \\ y\text{ }>\text{ }\frac{3}{4}x\text{ + 2} \end{gathered}[/tex]
To find the coordinate that satisfies the inequalities, we would obtain plots of the inequalities on a graph.
First, we obtain two points on the line: y = 2x - 4
when x = 0:
[tex]\begin{gathered} y\text{ = 2}\times0-4 \\ =\text{ -4} \end{gathered}[/tex]
when y = 0:
[tex]\begin{gathered} 0\text{ = 2x - 4} \\ 2x\text{ = 4} \\ x\text{ = 2} \end{gathered}[/tex]
We have the points (0, -4) and (2, 0)
The graph of the inequality is shown below:
Similarly for the line: y = 3/4x + 2:
when x = 0:
[tex]\begin{gathered} y\text{ = }\frac{3}{4}\text{ }\times0\text{ + 2} \\ =\text{ 2} \end{gathered}[/tex]
when y = 0:
[tex]\begin{gathered} 0\text{ = }\frac{3}{4}x\text{ + 2} \\ \frac{3}{4}x\text{ = -2} \\ x\text{ = }\frac{4}{3}\times-2 \\ =\text{ -}\frac{8}{3} \end{gathered}[/tex]
We have the points: (0, 2) and (-8/3, 0)
The graph of the inequality is shown below:
Combining the two inequality graphs:
The region that satisfies the given inequalities is the region with a mix of blue and green and this is our solution.
