Question

Which is true about the solution to the system of inequalities shown?

y < One-thirdx – 1

y < One-thirdx – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (0, negative 1) and (2, 0). Everything below the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (3, negative 2). Everything below the line is shaded.
All values that satisfy y < One-thirdx – 1 are solutions.
All values that satisfy y < One-thirdx – 3 are solutions.
All values that satisfy either y < One-thirdx – 1 or y < One-thirdx – 3 are solutions.

Answer 1

All values that satisfy y < (1/3)x − 3.

Reason: the solution is the intersection of the two shaded regions, so y must be less than both (1/3)x − 1 and (1/3)x − 3. Since (1/3)x − 3 < (1/3)x − 1 for every x, the stronger condition is y < (1/3)x − 3, which automatically implies y < (1/3)x − 1.