Problem 28 Graph the solution set of each s... [FREE SOLUTION]

Chapter 5: Problem 28

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}3 x+6 y \leq 6 \\\2 x+y \leq 8\end{array}\right.$$

Short Answer

Expert verified

The solution to the system of inequalities is the overlapping region between the two shaded areas from step 1 and 2.

Step by step solution

Graph the first inequality

First, graph the inequality $3x+6y \leq 6$. To do this, we first change the inequality into the form $y \leq mx+b$, where m is the slope and b is the y-intercept. By dividing throughout by 6, we get $y \leq -0.5x + 1$. This tells us that the line intersects with the y-axis at y=1 and has a slope of -0.5. Plot the line and shade the region including the line and to the bottom of it.

Graph the second inequality

For the second inequality $2x + y \leq 8$, change it to the form $y \leq mx + b$ by subtracting 2x from both sides. This gives us $y \leq -2x + 8$. This tells us that the line intersects with the y-axis at y=8 and has a slope of -2. Plot the line and shade the region including the line and to the bottom of it.

Find the overlapping region

The solution to the system of inequalities is the region where the shaded areas from step 1 and 2 overlap. This is the set of points that satisfy both inequalities.

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91影视

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}3 x+6 y \leq 6 \\\2 x+y \leq 8\end{array}\right.$$

Short Answer

Step by step solution

Graph the first inequality

Graph the second inequality

Find the overlapping region

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