Question

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. Give a point where both shades meet and points in between also tell if the line need to be shaded or not
y, is less than, x, plus, 2
y<x+2
y, is less than, minus, one half, x, minus, 4
y<−
2
1
​
x−4
x
y
x
y
Answer
Attempt 1 out of 2

Point: left parenthesis(
,
right parenthesis)

Answer 1

The two boundary lines are y = x + 2 and y = −(1/2)x − 4.
Solve x + 2 = −(1/2)x − 4 ⇒ (3/2)x = −6 ⇒ x = −4, y = −2. So the lines meet at (−4, −2).
Both inequalities are strict (<), so draw both lines dashed and shade the region below each line. The solution set is the overlap: points below both dashed lines.

A sample point in the solution set: (0, −5) (check: −5 < 0+2 and −5 < −4).
Other examples: (−3, −4), (−5, −6).