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.
There are no solutions.
Mark this and return

Answer 1

The solution to the system of inequalities y < One-thirdx – 1 and y < One-thirdx – 3, represented by two solid lines on a coordinate plane, is the set of all points that satisfy both inequalities simultaneously.

Since both inequalities have the same slope, One-third, but different y-intercepts, -1 and -3, the second inequality lies below the first. Therefore, the region that satisfies both inequalities is the region below the second line, which is also the region that satisfies the first inequality.

Thus, all values that satisfy y < One-thirdx – 3 are solutions to the system of inequalities. Therefore, the correct option is:

"All values that satisfy y < One-thirdx – 3 are solutions."