Question

graph the solution set of the following system of inequalities. 2x + 4y ≤ 4 3x + y ≤ 9 use the graphing tool to graph the system of inequalities. click to enlarge graph

Explanation:

Step1: Rewrite first - inequality in slope - intercept form

Solve $2x + 4y\leq4$ for $y$. Subtract $2x$ from both sides: $4y\leq - 2x + 4$. Then divide by 4: $y\leq-\frac{1}{2}x + 1$. The boundary line is $y =-\frac{1}{2}x + 1$, which has a y - intercept of 1 and a slope of $-\frac{1}{2}$. Since the inequality is $\leq$, the line is solid and we shade below the line.

Step2: Rewrite second - inequality in slope - intercept form

Solve $3x + y\leq9$ for $y$. Subtract $3x$ from both sides: $y\leq - 3x+9$. The boundary line is $y=-3x + 9$, which has a y - intercept of 9 and a slope of - 3. Since the inequality is $\leq$, the line is solid and we shade below the line.

Step3: Find the intersection region

The solution set of the system of inequalities is the region that satisfies both $y\leq-\frac{1}{2}x + 1$ and $y\leq - 3x+9$. This is the region where the shaded areas of the two inequalities overlap.

Answer:

Graph the solid line $y =-\frac{1}{2}x + 1$ and shade below it, graph the solid line $y=-3x + 9$ and shade below it. The intersection of the two shaded regions is the solution set of the system of inequalities.