Solve the system of two linear inequalities graphically.
\[
\left\{\begin{array}{l}
x< 1 \\
x \geq-4
\end{array}\right.
\]
Step 1 of 3: Graph the solution set of the first linear inequality.
Answer
The solution to the system of inequalities is the intersection of the solution sets of the two inequalities. This is the region that is to the right of the line \(x=-4\) and to the left of the line \(x=1\). Therefore, the solution to the system of inequalities is \(-4\leq x<1\).
Step 1 ：First, we graph the inequality \(x<1\). This is a vertical line at \(x=1\), and since the inequality is less than (and not less than or equal to), we draw a dashed line to indicate that the points on the line are not included in the solution set. The solution set for this inequality is all the points to the left of the line \(x=1\).
Step 2 ：Next, we graph the inequality \(x\geq-4\). This is a vertical line at \(x=-4\), and since the inequality is greater than or equal to, we draw a solid line to indicate that the points on the line are included in the solution set. The solution set for this inequality is all the points to the right of the line \(x=-4\).
Step 3 ：The solution to the system of inequalities is the intersection of the solution sets of the two inequalities. This is the region that is to the right of the line \(x=-4\) and to the left of the line \(x=1\). Therefore, the solution to the system of inequalities is \(-4\leq x<1\).
