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agining where the shading should be, identify which point would satisfy qualities. y<=(2)/(3)x+5, y>x+2

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Final answer:

To solve the given inequalities y<=(2/3)x+5 and y>x+2, graph the equations y=(2/3)x+5 and y=x+2 on the coordinate plane. Shade the region that satisfies both inequalities.

Step-by-step explanation:

In order to solve the given equations, we need to graph the inequalities y <= (2/3)x + 5 and y > x + 2 on the coordinate plane.

To do this, we can start by graphing the equations y = (2/3)x + 5 and y = x + 2 as dashed lines, since they are equal to the original inequalities. Then, we can determine which side of each line to shade based on the inequality symbol.

For the equation y <= (2/3)x + 5, we shade below the line, because the inequality symbol is <= (less than or equal to). For the equation y > x + 2, we shade above the line, because the inequality symbol is > (greater than).

The solution to the system of inequalities is the region that satisfies both inequalities, which is the shaded region where the shading crosses.

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