Question

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

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

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

(−1,1)
(
−
1
,
1
)
left parenthesis negative 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 the values of \( x \) and \( y \) from each ordered pair into the equation and check if the equation holds true.

1. **For the ordered pair \( (0, 2) \)**:
- \( x = 0 \), \( y = 2 \)
- Substitute: \( 3(0) - 8 = -4(2) \)
- Simplifies to: \( -8 = -8 \) (True)

2. **For the ordered pair \( (1, 1) \)**:
- \( x = 1 \), \( y = 1 \)
- Substitute: \( 3(1) - 8 = -4(1) \)
- Simplifies to: \( 3 - 8 = -4 \)
- Which is: \( -5 \neq -4 \) (False)

3. **For the ordered pair \( (-1, 1) \)**:
- \( x = -1 \), \( y = 1 \)
- Substitute: \( 3(-1) - 8 = -4(1) \)
- Simplifies to: \( -3 - 8 = -4 \)
- Which is: \( -11 \neq -4 \) (False)

4. **For the ordered pair \( (0, -2) \)**:
- \( x = 0 \), \( y = -2 \)
- Substitute: \( 3(0) - 8 = -4(-2) \)
- Simplifies to: \( -8 = 8 \) (False)

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

Thus, the correct answer is **(0, 2)**.