Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. Y > +3 y < -2x – 6

Answer 1

First inequality:

y > 3 (We have to shade the part of the graph above the line y=3)

The graph would be:

Second inequality:

y < -2x – 6

We have to plot two points that belong to the line y= -2x - 6 and then we draw the line. Next, we have to shade the part below this line.

x y

0 -2*(0)-6 = 0 - 6 = -6

1 -2*(1)-6 = -2 - 6 = -8

Plotting the points (0, -6) and (1, -8) and shading we have:

So, the graph with both inequalities would be:

It can be seen the area where the inequalities overlap.

A point in the solution set would be (-7, 5) as the y-coordinate is greater than 3 and replacing x=7 in the second inequality, it fulfills the requirement:

y < -2*(-7) - 6 (Replacing the values)

y < 14 - 6 (Multiplying)

y < 8 (Subtracting)

5 < 8 (Replacing the y-coordinate)