Question
Which ordered pair is a solution to the system of linear equations?
x + 4y = 3
y = −4x − 3
(1, 1)
(1, −1)
(−1, 1)
(−1, −1)
x + 4y = 3
y = −4x − 3
(1, 1)
(1, −1)
(−1, 1)
(−1, −1)
Answers
Answered by
GPT-4o mini
To determine which ordered pair is a solution to the system of linear equations, we can substitute each pair into both equations and check for validity.
We have the equations:
1. \( x + 4y = 3 \)
2. \( y = -4x - 3 \)
Let's test each ordered pair:
1. **Pair (1, 1)**:
- Substitute into the first equation: \( 1 + 4(1) = 1 + 4 = 5 \) (not equal to 3, so it doesn't satisfy).
2. **Pair (1, -1)**:
- Substitute into the first equation: \( 1 + 4(-1) = 1 - 4 = -3 \) (not equal to 3, so it doesn't satisfy).
3. **Pair (−1, 1)**:
- Substitute into the first equation: \( -1 + 4(1) = -1 + 4 = 3 \) (equals 3, so it satisfies the first equation).
- Check the second equation: \( y = -4(-1) - 3 = 4 - 3 = 1 \) (it also satisfies the second equation).
4. **Pair (−1, −1)**:
- Substitute into the first equation: \( -1 + 4(-1) = -1 - 4 = -5 \) (not equal to 3, so it doesn't satisfy).
Based on our checks, the only ordered pair that satisfies both equations is:
**(−1, 1)**.
We have the equations:
1. \( x + 4y = 3 \)
2. \( y = -4x - 3 \)
Let's test each ordered pair:
1. **Pair (1, 1)**:
- Substitute into the first equation: \( 1 + 4(1) = 1 + 4 = 5 \) (not equal to 3, so it doesn't satisfy).
2. **Pair (1, -1)**:
- Substitute into the first equation: \( 1 + 4(-1) = 1 - 4 = -3 \) (not equal to 3, so it doesn't satisfy).
3. **Pair (−1, 1)**:
- Substitute into the first equation: \( -1 + 4(1) = -1 + 4 = 3 \) (equals 3, so it satisfies the first equation).
- Check the second equation: \( y = -4(-1) - 3 = 4 - 3 = 1 \) (it also satisfies the second equation).
4. **Pair (−1, −1)**:
- Substitute into the first equation: \( -1 + 4(-1) = -1 - 4 = -5 \) (not equal to 3, so it doesn't satisfy).
Based on our checks, the only ordered pair that satisfies both equations is:
**(−1, 1)**.