1. Solve the system by graphing on the coordinate plane. Indicate if there is no solution. \[ \left\{\begin{array}{c} y>2-x \\ y>\frac{2}{3} x-2 \end{array}\right. \]

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.