Solve the system of inequalities by graphing. \[ \begin{array}{l}y \leq-\frac{1}{3} x+7 \\ y \geq-x+3\end{array} \] Use the graphing tool to graph the system. Click to

It seems that the graphing tool is currently unavailable. However, I can guide you through the process of solving the system of inequalities by graphing them step by step. ### Step 1: Graph the first inequality The first inequality is: \[ y \leq -\frac{1}{3} x + 7 \] 1. **Find the y-intercept**: Set \(x = 0\): \[ y = -\frac{1}{3}(0) + 7 = 7 \] So, the y-intercept is (0, 7). 2. **Find another point**: Set \(y = 0\) to find the x-intercept: \[ 0 = -\frac{1}{3} x + 7 \implies \frac{1}{3} x = 7 \implies x = 21 \] So, the x-intercept is (21, 0). 3. **Draw the line**: Plot the points (0, 7) and (21, 0) and draw a dashed line since the inequality is "less than or equal to" (the line itself is included). 4. **Shade the region**: Shade below the line because \(y\) is less than or equal to the line. ### Step 2: Graph the second inequality The second inequality is: \[ y \geq -x + 3 \] 1. **Find the y-intercept**: Set \(x = 0\): \[ y = -0 + 3 = 3 \] So, the y-intercept is (0, 3). 2. **Find another point**: Set \(y = 0\) to find the x-intercept: \[ 0 = -x + 3 \implies x = 3 \] So, the x-intercept is (3, 0). 3. **Draw the line**: Plot the points (0, 3) and (3, 0) and draw a solid line since the inequality is "greater than or equal to" (the line itself is included). 4. **Shade the region**: Shade above the line because \(y\) is greater than or equal to the line. ### Step 3: Identify the solution region The solution to the system of inequalities is the region where the shaded areas overlap. This region represents all the points \((x, y)\) that satisfy both inequalities. If you have graphing software or graph paper, you can plot these lines and shade the appropriate regions to visualize the solution. If you need further assistance or have any questions, feel free to ask!