Question

The ordered pair (-1, 1) is a solution to which system of inequalities(1 point)
Responses

{x+y≥24x+y≥−1

{y>4x−3y≥−2x+3

{y≥−5x+3y>−2

{y≥x−3y≥−x−1

Answer 1

To determine which system of inequalities has (-1, 1) as a solution, we need to substitute \(x = -1\) and \(y = 1\) into each inequality of the systems provided.

**1. System:**
\[
\begin{cases}
x + y \geq 2 \\
x + y \geq -1
\end{cases}
\]
- First inequality: \(-1 + 1 \geq 2\) → \(0 \geq 2\) (False)
- Second inequality: \(-1 + 1 \geq -1\) → \(0 \geq -1\) (True)

**2. System:**
\[
\begin{cases}
y > 4x - 3 \\
y \geq -2x + 3
\end{cases}
\]
- First inequality: \(1 > 4(-1) - 3\) → \(1 > -4 - 3\) → \(1 > -7\) (True)
- Second inequality: \(1 \geq -2(-1) + 3\) → \(1 \geq 2 + 3\) → \(1 \geq 5\) (False)

**3. System:**
\[
\begin{cases}
y \geq -5x + 3 \\
y > -2
\end{cases}
\]
- First inequality: \(1 \geq -5(-1) + 3\) → \(1 \geq 5 + 3\) → \(1 \geq 8\) (False)
- Second inequality: \(1 > -2\) (True)

**4. System:**
\[
\begin{cases}
y \geq x - 3 \\
y \geq -x - 1
\end{cases}
\]
- First inequality: \(1 \geq -1 - 3\) → \(1 \geq -4\) (True)
- Second inequality: \(1 \geq -(-1) - 1\) → \(1 \geq 1\) (True)

Based on this substitution, the only system that has both inequalities true when the ordered pair (-1, 1) is used is the fourth system:
\[
\begin{cases}
y \geq x - 3 \\
y \geq -x - 1
\end{cases}
\]
Thus, the answer is:

**{y ≥ x - 3, y ≥ -x - 1}**