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Multiple Choice
Graph the system of inequalities and indicate the region (if any) of solutions satisfying all equations.
3x−2y>6
3x−2y < −4
A
B
C
D
Verified step by step guidance
1
Start by rewriting the given inequalities in slope-intercept form (y = mx + b). For the first inequality, 3x - 2y > 6, solve for y to get y < (3/2)x - 3.
For the second inequality, 3x - 2y < -4, solve for y to get y > (3/2)x + 2.
Graph the line y = (3/2)x - 3. Since the inequality is y < (3/2)x - 3, use a dashed line to indicate that points on the line are not included in the solution. Shade the region below this line.
Graph the line y = (3/2)x + 2. Since the inequality is y > (3/2)x + 2, use a dashed line to indicate that points on the line are not included in the solution. Shade the region above this line.
The solution to the system of inequalities is the region where the shaded areas overlap. This is the region between the two lines, not including the lines themselves.