Question

Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y
.(1 point)
Responses

(0,2)
left parenthesis 0 comma 2 right parenthesis

(1,1)
left parenthesis 1 comma 1 right parenthesis

(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

(0,−2)

Answer 1

To determine which ordered pair is a solution to the equation \(3x - 8 = -4y\), we can substitute the values of \(x\) and \(y\) from each ordered pair into the equation and see if it holds true.

1. **For (0, 2):**
\[
x = 0,\ y = 2 \\
3(0) - 8 = -4(2) \\
-8 = -8 \quad \text{(True)}
\]

2. **For (1, 1):**
\[
x = 1,\ y = 1 \\
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 = -4 \quad \text{(False)}
\]

3. **For (−1, 1):**
\[
x = -1,\ y = 1 \\
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 = -4 \quad \text{(False)}
\]

4. **For (0, -2):**
\[
x = 0,\ y = -2 \\
3(0) - 8 = -4(-2) \\
-8 = 8 \quad \text{(False)}
\]

The only ordered pair that satisfies the equation \(3x - 8 = -4y\) is \((0, 2)\).

**Answer: (0, 2)**