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 the Points on where each inequality should be graphed also give the shading for both inequality's and points within the 2 inequality's shading
y, is greater than, minus, one half, x, minus, 3
y>−
2
1
​
x−3
y, is greater than, x, plus, 6
y>x+6
x
y
x
y
Answer
Attempt 1 out of 2

Point: left parenthesis(
,
right parenthesis) Submit Answer

Answer 1

Steps to graph:

1. Graph the boundary lines as dashed (strict >):
- y = −(1/2)x − 3: plot (0, −3) and (2, −4) (or (−6, 0)). Draw a dashed line through them.
- y = x + 6: plot (0, 6) and (−6, 0). Draw a dashed line through them.

(Note: the two lines meet at (−6, 0).)

2. Shade above each dashed line (because both are “>”). The solution set is the region that is above both lines — i.e. above the higher line at each x (the wedge above their intersection).

A point inside the solution region: (0, 7) since 7 > 0 + 6 and 7 > −(1/2)(0) − 3.

Answer
Point: (0, 7)