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

Explanation:

Step1: Graph the line $y = 2x+4$

The line $y = 2x + 4$ has a y - intercept of 4 and a slope of 2. Since the inequality is $y>2x + 4$, we draw a dashed line (because the points on the line are not included in the solution) using the slope - intercept form to plot points. For example, when $x = 0$, $y=4$ and when $x=-2$, $y = 0$.

Step2: Shade the region for $y>2x + 4$

We choose a test point not on the line, say $(0,0)$. Substitute into the inequality: $0>2(0)+4$ gives $0 > 4$, which is false. So we shade the region above the line $y = 2x+4$.

Step3: Graph the line $x + y=6$

Rewrite it in slope - intercept form $y=-x + 6$. It has a y - intercept of 6 and a slope of - 1. When $x = 0$, $y = 6$ and when $y = 0$, $x=6$. Since the inequality is $x + y\leqslant6$, we draw a solid line (because the points on the line are included in the solution).

Step4: Shade the region for $x + y\leqslant6$

Choose a test point, say $(0,0)$. Substitute into the inequality: $0+0\leqslant6$, which is true. So we shade the region below the line $x + y = 6$.

Step5: Identify the solution region

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

Answer:

Graph a dashed line $y = 2x+4$ and shade the region above it, graph a solid line $x + y=6$ and shade the region below it. The overlapping shaded region is the solution.