1. **Stating the problem:** We need to find the solution region for the system of inequalities: (a) \(x + y \geq 4\) \(2x - y < 6\) 2. **Step 1: Graph the first inequality \(x + y \geq 4\)** - Rewrite as \(y \geq 4 - x\). - Find intercepts: - When \(x=0\), \(y=4\) gives point \((0,4)\). - When \(y=0\), \(x=4\) gives point \((4,0)\). - Draw the line through \((0,4)\) and \((4,0)\). - Since inequality is \(\geq\), shade the region above or on the line. 3. **Step 2: Graph the second inequality \(2x - y < 6\)** - Rewrite as \(y > 2x - 6\). - Find intercepts: - When \(x=0\), \(y > -6\) (point \((0,-6)\)). - When \(y=0\), solve \(2x = 6\) gives \(x=3\) (point \((3,0)\)). - Draw the line \(y = 2x - 6\) through \((0,-6)\) and \((3,0)\). - Since inequality is strict \(<\), the line is dashed. - Shade the region above the line (because \(y > 2x - 6\)). 4. **Step 3: Find the feasible region** - The solution is the intersection of the shaded regions from steps 2 and 3. 5. **Summary:** - The feasible region is the area on or above the line \(x + y = 4\) and strictly above the line \(y = 2x - 6\).