Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le \frac{-1}{2}x+3\\ y<1\end{array}\right.$

Short answer

• The solution set of the system is the area shaded in darker color including the solid line.

Step-by-step solution

Step 1. Given Information

The given system is$\left\{\begin{array}{l}y\le \frac{-1}{2}x+3\\ y<1\end{array}\right.$.

Step 2. Plot the first inequality

• The intercepts of $y=\frac{-1}{2}x+3$are $(0,3),(6,0)$.
• Join the points to plot a solid line.
• The point $(0,0)$satisfies the inequality, so shade the region that includes the origin.

Step 3. Plot the second inequality 

• The line $y=1$will be a horizontal line passing through $(0,1)$.
• Draw a dotted horizontal 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 including the solid line.

Step 4. Check the Solution

• One of the points that lie in the solution set is $(0,0)$.
• It has already been verified that the point $(0,0)$satisfies both the inequalities.

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