Which ordered pair is in the solution set of the system of linear inequalities?

Question

y > Three-halvesx – 1

y < Three-halvesx – 1

On a coordinate plane, 2 dashed straight lines are shown. The first line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the right of the line is shaded. The second line has a positive slope and goes through (0, negative 1) and (2, 2). Everything to the left of the line is shaded.
(–5, 2)
(2, 2)
(5, 2)
no solution

Answer 1

To find which ordered pair is in the solution set of the given system of inequalities, let's first analyze the inequalities:

1. \(y > \frac{3}{2}x - 1\)
2. \(y < \frac{3}{2}x - 1\)

The first inequality \(y > \frac{3}{2}x - 1\) indicates the region above the line, while the second inequality \(y < \frac{3}{2}x - 1\) indicates the region below the line.

Since both inequalities refer to the same line \(y = \frac{3}{2}x - 1\) but specify different regions (one above and one below), there are no points that can satisfy both inequalities simultaneously. This means there is no solution.

As a result, the answer is:

no solution.