Question
Graph the system of inequalities.
y > 2x - 2 2y - x <= 10
y > 2x - 2 2y - x <= 10
Answers
GPT 3.5
To graph the system of inequalities, we will graph the individual inequalities and find the region where they overlap.
First, let's graph the inequality y > 2x - 2:
1. Graph the line y = 2x - 2, which has a slope of 2 and a y-intercept of -2.
2. Since this inequality is "greater than," the line should be dotted to indicate that the line itself is not included in the solution.
3. Shade the region above the line to represent y > 2x - 2.
Next, let's graph the inequality 2y - x <= 10:
1. Graph the line 2y - x = 10 by finding its x-intercept and y-intercept.
When x = 0, 2y = 10, so y = 5 (y-intercept)
When y = 0, 2(0) - x = 10, so x = -10 (x-intercept)
Therefore, the line passes through the points (0, 5) and (-10, 0).
2. Since this inequality is "less than or equal to," the line should be a solid line.
3. Shade the region below the line to represent 2y - x <= 10.
The graph will show the region where the two shaded areas overlap, indicating the solution to the system of inequalities.
(Note: Due to the limitations of text-based responses, I'm unable to provide an actual graph. Hence, I highly recommend referring to a graphing tool or software to visualize the solution graphically.
First, let's graph the inequality y > 2x - 2:
1. Graph the line y = 2x - 2, which has a slope of 2 and a y-intercept of -2.
2. Since this inequality is "greater than," the line should be dotted to indicate that the line itself is not included in the solution.
3. Shade the region above the line to represent y > 2x - 2.
Next, let's graph the inequality 2y - x <= 10:
1. Graph the line 2y - x = 10 by finding its x-intercept and y-intercept.
When x = 0, 2y = 10, so y = 5 (y-intercept)
When y = 0, 2(0) - x = 10, so x = -10 (x-intercept)
Therefore, the line passes through the points (0, 5) and (-10, 0).
2. Since this inequality is "less than or equal to," the line should be a solid line.
3. Shade the region below the line to represent 2y - x <= 10.
The graph will show the region where the two shaded areas overlap, indicating the solution to the system of inequalities.
(Note: Due to the limitations of text-based responses, I'm unable to provide an actual graph. Hence, I highly recommend referring to a graphing tool or software to visualize the solution graphically.