Question

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

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Only values that satisfy y > 3x + 1 are solutions.
Only values that satisfy y < 3x – 3 are solutions.
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
There are no solutions.

Answer 1

There are no solutions.

Reason: any solution would have to satisfy 3x + 1 < y < 3x − 3. That would imply 3x + 1 < 3x − 3, i.e. 1 < −3, which is impossible. So the shaded regions do not overlap.