Question

graph the solution set of the following system of inequalities.
3x + 6y ≤ 6
5x + y ≤ 10
use the graphing tool to graph the system of inequalities.

Explanation:

Step1: Rewrite first - inequality in slope - intercept form

Solve $3x + 6y\leq6$ for $y$. First, subtract $3x$ from both sides: $6y\leq - 3x + 6$. Then divide by 6: $y\leq-\frac{1}{2}x + 1$.

Step2: Rewrite second - inequality in slope - intercept form

Solve $5x + y\leq10$ for $y$. Subtract $5x$ from both sides: $y\leq - 5x+10$.

Step3: Graph the first line

The line $y =-\frac{1}{2}x + 1$ has a y - intercept of 1 and a slope of $-\frac{1}{2}$. Since the inequality is $y\leq-\frac{1}{2}x + 1$, we shade the region below the line.

Step4: Graph the second line

The line $y=-5x + 10$ has a y - intercept of 10 and a slope of - 5. Since the inequality is $y\leq - 5x+10$, we shade the region below the line.

Step5: Find the intersection region

The solution set of the system of inequalities is the region that is shaded for both inequalities, which is the region that is below both $y =-\frac{1}{2}x + 1$ and $y=-5x + 10$.

Answer:

Graph the line $y =-\frac{1}{2}x + 1$ and shade below it, graph the line $y=-5x + 10$ and shade below it. The solution set is the overlapping shaded region.