Graphing Inequalities

Question

What is the graph and solution for this system?

 y > 3x - 3

3y - x < or equal to 6

Answer 1

Let's start by turning the second equation into slope-intercept form:

3y - x ≤ 6

3y ≤ x + 6

y ≤ ¹/₃ x + 2

 

Now you need to graph the two lines. Remember: with the y ≤ ¹/₃ x + 2 you use a full line while the
y > 3x - 3 uses a dash line.

 

From there you shade in the areas that are above the y > 3x - 3, below y ≤ ¹/₃ x + 2, AND ONLY fulfills those two inequalities. If the shaded area passes through another line, stop. After they intersect and the shaded area wouldn't touch the other line at all, stop. You stop because they would only be answerable to one of the inequalities, but not both of them.