which graph represents this system of inequalities?
y<=2x+3
3x+y<=-2
In order to determine which graph represents this system of inequalities, we need to first graph each individual inequality and then determine which graph contains the overlapping region that represents the solution to the entire system.
1. Graph the inequality y ≤ 2x + 3:
To graph this inequality, start by graphing the line y = 2x + 3. This line has a y-intercept of 3 and a slope of 2 (rise of 2 and run of 1). Since the inequality includes the equality symbol ≤, we should also draw a solid line. Shade the region below the line to represent y ≤ 2x + 3.
2. Graph the inequality 3x + y ≤ -2:
To graph this inequality, start by graphing the line 3x + y = -2. Rearranging the equation, we get y = -3x - 2. This line has a y-intercept of -2 and a slope of -3 (rise of -3 and run of 1). Since the inequality includes the equality symbol ≤, we should also draw a solid line. Shade the region below the line to represent 3x + y ≤ -2.
The overlapping region that represents the solution to the entire system is the shaded region where both inequalities overlap. Therefore, the correct graph would be the one that includes the overlapping shaded region.