graph of the following system of equations? ) 2x-3ylt 12 ygeqslant -(1)/(2)x+5

To graph the system of inequalities, we need to plot the boundary lines and then determine the regions that satisfy each inequality.<br /><br />1. For the first inequality, $2x-3y<12$, we can rewrite it as $y>\frac{2}{3}x-4$. This is a line with a slope of $\frac{2}{3}$ and a y-intercept of -4. Since the inequality is strict, we will draw a dashed line to represent the boundary.<br /><br />2. For the second inequality, $y\geqslant -\frac{1}{2}x+5$, this is a line with a slope of $-\frac{1}{2}$ and a y-intercept of 5. Since the inequality is non-strict, we will draw a solid line to represent the boundary.<br /><br />Now, let's plot these lines on a coordinate plane and determine the regions that satisfy each inequality.<br /><br />Step 1: Plot the line $y=\frac{2}{3}x-4$ as a dashed line.<br />Step 2: Plot the line $y=-\frac{1}{2}x+5$ as a solid line.<br />Step 3: Determine the region that satisfies $y>\frac{2}{3}x-4$. This region is above the dashed line.<br />Step 4: Determine the region that satisfies $y\geqslant -\frac{1}{2}x+5$. This region is above the solid line.<br /><br />The solution to the system of inequalities is the region where the two shaded regions overlap.