Answer: To graph the system, we will first graph each inequality separately and then look for the region of overlap.
For the inequality 3x - y ≤ 3, we can rearrange it to get y ≥ 3x - 3. This is the equation of a line with a y-intercept of -3 and a slope of 3. We can graph this line by plotting the y-intercept and then using the slope to find additional points.
For the inequality y ≥ -1/2x, we can rewrite it as y + 1/2x ≥ 0. This is the equation of a line with a y-intercept of 0 and a slope of -1/2. We can graph this line by plotting the y-intercept and then using the slope to find additional points.
Once we have both lines graphed, we can shade in the region of overlap.
Here's a visual representation of the graph:
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3x - y = 3
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y = -1/2x
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The region of overlap is the shaded region below the line y = -1/2x and above the line 3x - y = 3.
Therefore, the solution to the system is all points in the shaded region. We can write this solution as:
(x,y)
Explanation: