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 of the ordered pairs is a solution to the equation \( 3x - 8 = -4y \), we will substitute each pair \((x, y)\) into the equation and check if both sides are equal.

1. For the pair \((-1, 1)\):
\[
3(-1) - 8 = -4(1)
\]
\[
-3 - 8 = -4
\]
\[
-11 \neq -4 \quad \text{(Not a solution)}
\]

2. For the pair \((0, -2)\):
\[
3(0) - 8 = -4(-2)
\]
\[
-8 = 8
\]
\[
-8 \neq 8 \quad \text{(Not a solution)}
\]

3. For the pair \((1, 1)\):
\[
3(1) - 8 = -4(1)
\]
\[
3 - 8 = -4
\]
\[
-5 \neq -4 \quad \text{(Not a solution)}
\]

4. For the pair \((0, 2)\):
\[
3(0) - 8 = -4(2)
\]
\[
-8 = -8
\]
\[
-8 = -8 \quad \text{(This is a solution)}
\]

The ordered pair \((0, 2)\) is the only one that satisfies the equation. Thus, the solution is:

\((0, 2)\)