Question
Give me 10 linear equations that have no solution
Answers
GPT-4o mini
Linear equations that have no solution typically represent parallel lines, which means they never intersect. Here are 10 examples of such linear equations:
1. \( 2x + 3y = 6 \)
2. \( 4x + 6y = 12 \)
(Equations 1 and 2 represent the same line; they are dependent and would intersect infinitely, so let's replace 2.)
2. \( 2x + 3y = 6 \)
3. \( 2x + 3y = 8 \)
4. \( x - 2y = 5 \)
5. \( x - 2y = 7 \)
6. \( 3x + y = 4 \)
7. \( 3x + y = 10 \)
8. \( 5x - 2y = 1 \)
9. \( 5x - 2y = 3 \)
10. \( -x + 4y = 12 \)
11. \( -x + 4y = 15 \)
Each pair above (e.g., equations 1 & 3, 4 & 5, etc.) is an example of parallel lines with the same slope but different y-intercepts, meaning they have no solution.
1. \( 2x + 3y = 6 \)
2. \( 4x + 6y = 12 \)
(Equations 1 and 2 represent the same line; they are dependent and would intersect infinitely, so let's replace 2.)
2. \( 2x + 3y = 6 \)
3. \( 2x + 3y = 8 \)
4. \( x - 2y = 5 \)
5. \( x - 2y = 7 \)
6. \( 3x + y = 4 \)
7. \( 3x + y = 10 \)
8. \( 5x - 2y = 1 \)
9. \( 5x - 2y = 3 \)
10. \( -x + 4y = 12 \)
11. \( -x + 4y = 15 \)
Each pair above (e.g., equations 1 & 3, 4 & 5, etc.) is an example of parallel lines with the same slope but different y-intercepts, meaning they have no solution.