Question

Determine whether the ordered pair is a solution of the given system
(2,-1); 3-3y less then or equal to 3y
3y greater then 2x + 1

Answer 1

To determine if the ordered pair (2, -1) is a solution for the system of inequalities, we will substitute \(x = 2\) and \(y = -1\) into both inequalities and check if they hold true.

The inequalities given are:

1. \(3 - 3y \leq 3y\)
2. \(3y > 2x + 1\)

**Step 1: Check the first inequality.**

Substitute \(y = -1\):
\[
3 - 3(-1) \leq 3(-1)
\]
\[
3 + 3 \leq -3
\]
\[
6 \leq -3
\]

This statement is **false**.

**Step 2: Check the second inequality.**

Substitute \(x = 2\) and \(y = -1\):
\[
3(-1) > 2(2) + 1
\]
\[
-3 > 4 + 1
\]
\[
-3 > 5
\]

This statement is also **false**.

Since the ordered pair (2, -1) does not satisfy both inequalities, we conclude that it is **not a solution** of the given system.