use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x +…

Explanation:

Step1: Graph $y > 2x + 4$

First, graph the line $y=2x + 4$. Since the inequality is $y>2x + 4$, the line will be dashed (because the points on the line are not included in the solution). The $y$-intercept is 4 and the slope is 2. Then, test a point not on the line, say $(0,0)$. Substitute into the inequality: $0>2(0)+4$ gives $0 > 4$ which is false. So, shade the region above the line.

Step2: Graph $x + y\leq6$

Rewrite the inequality as $y\leq -x + 6$. Graph the line $y=-x + 6$. Since the inequality is $\leq$, the line will be solid. The $y$-intercept is 6 and the slope is - 1. Test the point $(0,0)$: $0+0\leq6$ which is true. So, shade the region below the line.

Step3: Find the solution region

The solution to the system of inequalities is the region that is shaded for both inequalities. It is the intersection of the region above $y = 2x+4$ and the region below $y=-x + 6$.

Answer:

The solution is the intersection of the region above the dashed line $y = 2x+4$ and the region below the solid line $y=-x + 6$.