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 negative 1 comma 1 right parenthesis (1,1) left parenthesis 1 comma 1 right parenthesis (0,−2)

Answer 1

To determine which ordered pair is a solution to the equation \( 3x - 8 = -4y \), we will substitute each pair into the equation.

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

2. For the pair \( (-1, 1) \):
\[
x = -1, \quad y = 1
\]
\[
3(-1) - 8 = -4(1) \implies -3 - 8 = -4 \implies -11 \neq -4 \quad \text{(False)}
\]

3. For the pair \( (1, 1) \):
\[
x = 1, \quad y = 1
\]
\[
3(1) - 8 = -4(1) \implies 3 - 8 = -4 \implies -5 \neq -4 \quad \text{(False)}
\]

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

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