Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}3x-4y<8\\ x<1\end{array}\right.$

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$\left\{\begin{array}{l}3x-4y<8\\ x<1\end{array}\right.$.

Step 2. Plot the first inequality 

• The intercepts of $3x-4y=8$are $(0,-2),\left(\frac{8}{3},0\right)$.
• Join the points to plot a dotted line.
• The point $(0,0)$satisfies the inequality, so shade the region that includes 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 $(-1,-1)$.
• Check if the point satisfies the inequalities.

$$\begin{gathered} -3-4\stackrel{?}{<}8 \\ -7<8 \end{gathered}$$

$-1<1$

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