Question

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

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

(0,−2)
left parenthesis 0 comma negative 2 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 can substitute each pair into the equation and see if both sides are equal.

1. **For the pair \((-1, 1)\)**:
\[
x = -1, \quad y = 1
\]
Substitute into the equation:
\[
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 \neq -4 \quad \text{(not a solution)}
\]

2. **For the pair \((0, -2)\)**:
\[
x = 0, \quad y = -2
\]
Substitute into the equation:
\[
3(0) - 8 = -4(-2) \\
0 - 8 = 8 \\
-8 \neq 8 \quad \text{(not a solution)}
\]

3. **For the pair \((1, 1)\)**:
\[
x = 1, \quad y = 1
\]
Substitute into the equation:
\[
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 \neq -4 \quad \text{(not a solution)}
\]

4. **For the pair \((0, 2)\)**:
\[
x = 0, \quad y = 2
\]
Substitute into the equation:
\[
3(0) - 8 = -4(2) \\
0 - 8 = -8 \\
-8 = -8 \quad \text{(this is a solution)}
\]

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