1. Solve the system by graphing on the coordinate plane. Indicate if there is no solution.
\[
\left\{\begin{array}{c}
y> 2-x \\
y> \frac{2}{3} x-2
\end{array}\right.
\]
The solution to the system of inequalities is the region where the two shaded areas overlap.
Step 1 :First, we need to graph the two inequalities on the coordinate plane. The first inequality, \(y > 2 - x\), is a line with a slope of -1 and a y-intercept of 2. The second inequality, \(y > \frac{2}{3}x - 2\), is a line with a slope of \(\frac{2}{3}\) and a y-intercept of -2.
Step 2 :We graph these two lines and shade the region above each line because the inequalities are 'greater than'.
Step 3 :The solution to the system of inequalities is the region where the shaded areas overlap. If there is no overlap, then the system has no solution.
Step 4 :After graphing, we find that the two shaded regions do overlap, indicating that there is a solution to the system of inequalities.
Step 5 :The solution to the system of inequalities is the region where the two shaded areas overlap.