Question

Graph the solution to the following system of inequalities:

1. y < -5
2. 5x + 6y < 18

Answer 1

To graph the given system of inequalities, graph the horizontal line y = -5 and shade below it for y < -5. Then graph the line y = (-5/6)x + 3 with a dashed line and shade below it for 5x + 6y < 18. The solution is the overlapped shaded area.

Step-by-step explanation:

To graph the solution to the system of inequalities y < -5 and 5x + 6y < 18, follow these steps:

1. Start with graphing the first inequality y < -5. This is a horizontal line at y = -5. Since the inequality is less than, shade everything below this line.
2. Next, rearrange the second inequality to solve for y: 5x + 6y < 18 becomes 6y < -5x + 18, which simplifies to y < (-5/6)x + 3. To graph this, find the y-intercept by setting x to 0, giving us the point (0, 3). Plot this point on the graph.
3. Now determine the slope, which is -5/6. Starting from the y-intercept, move down 5 units and right 6 units to find another point on the line. Plot this second point.
4. Draw a dashed line through the two points since the inequality is less than, not “less than or equal to”. Again, shade the area below this line since y is less than the expression.
5. The solution to the system of inequalities will be where the shaded regions of both inequalities overlap.