Question

Determine which of the following ordered pairs is a solution to the equation 3x - 8 = - 4y
(1, 1)
(- 1, 1)
(0, - 2)
(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 into the equation and check if both sides are equal.

1. For the ordered pair \( (1, 1) \):
\[
x = 1, \quad y = 1
\]
Substitute into the equation:
\[
3(1) - 8 = -4(1)
\]
Simplifying both sides:
\[
3 - 8 = -4 \quad \Rightarrow \quad -5 \neq -4 \quad \text{(Not a solution)}
\]

2. For the ordered pair \( (-1, 1) \):
\[
x = -1, \quad y = 1
\]
Substitute into the equation:
\[
3(-1) - 8 = -4(1)
\]
Simplifying both sides:
\[
-3 - 8 = -4 \quad \Rightarrow \quad -11 \neq -4 \quad \text{(Not a solution)}
\]

3. For the ordered pair \( (0, -2) \):
\[
x = 0, \quad y = -2
\]
Substitute into the equation:
\[
3(0) - 8 = -4(-2)
\]
Simplifying both sides:
\[
-8 = 8 \quad \Rightarrow \quad -8 \neq 8 \quad \text{(Not a solution)}
\]

4. For the ordered pair \( (0, 2) \):
\[
x = 0, \quad y = 2
\]
Substitute into the equation:
\[
3(0) - 8 = -4(2)
\]
Simplifying both sides:
\[
-8 = -8 \quad \Rightarrow \quad \text{(This is a solution)}
\]

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