Question

solve the system of inequalities by graphing.
( y < -2 )
( x < 6 )
select a line to change it between solid and dotted. select a region to shade it.

Explanation:

Step1: Analyze \( y < -2 \)

The inequality \( y < -2 \) represents a horizontal line \( y = -2 \) (dotted, since \( < \) not \( \leq \)) and the region below this line (where \( y \)-values are less than -2).

Step2: Analyze \( x < 6 \)

The inequality \( x < 6 \) represents a vertical line \( x = 6 \) (dotted, since \( < \) not \( \leq \)) and the region to the left of this line (where \( x \)-values are less than 6).

Step3: Shade the Intersection

The solution to the system is the region that satisfies both inequalities. So we shade the area that is below \( y = -2 \) and to the left of \( x = 6 \). The lines \( y = -2 \) and \( x = 6 \) should be dotted (as the inequalities are strict, \( < \) not \( \leq \)).

Answer:

• For \( y < -2 \): Draw a dotted horizontal line at \( y = -2 \) and shade the region below it.
• For \( x < 6 \): Draw a dotted vertical line at \( x = 6 \) and shade the region to the left of it.
• The solution region is the overlapping area (below \( y = -2 \) and left of \( x = 6 \)).