Question

Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y .
(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

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

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

(0,2)

Answer 1

To determine which ordered pairs are solutions to the equation \( 3x - 8 = -4y \), we will substitute the \( x \) and \( y \) values of each ordered pair into the equation and see if both sides of the equation 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 \((1, 1)\):**
\[
x = 1, \quad y = 1
\]
Substitute into the equation:
\[
3(1) - 8 = -4(1)
\]
\[
3 - 8 = -4
\]
\[
-5 \neq -4 \quad \text{(not a solution)}
\]

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

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

The only solution from the provided ordered pairs is \((0, 2)\).