Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}-3x+5y>10\\ x>-1\end{array}\right.$

Short answer

• The solution set of the system is the area shaded in darker color excluding the boundary.

Step-by-step solution

Step 1. Given information

The given system is$\left\{\begin{array}{l}-3x+5y>10\\ x>-1\end{array}\right.$.

Step 2. Plot the first inequality

• The intercepts of $-3x+5y=10$are $(0,2),\left(\frac{-10}{3},0\right)$.
• Join the points to plot a dotted line.
• The point $(0,0)$does not satisfy the inequality, so shade the region that excludes the origin.

Step 3. Plot the second inequality

• The line $x=-1$will be a vertical line passing through $(-1,0)$.
• Draw a dotted vertical line on the same graph.
• The point $(0,0)$satisfies the inequality, so shade the region that includes the origin.

• The solution set of the system is the area shaded in darker color excluding the boundary.

Step 4. Check the Solution

• One of the points that lie in the solution set is $(0,4)$.
• Check if the point satisfies the inequalities.

$$\begin{gathered} 0+5\left(4\right)\stackrel{?}{>}10 \\ 20>10 \\ 0>-1 \end{gathered}$$

• As both the inequalities are satisfied, the solution is verified.