Question

Which two equations form a system with no * solutions (same slope but different y intercept)?
1. y = 5х -4
2. у =-2x + 3
3. y =37 + 1
4. 2y = 6x + 2
5. у - 5х = 2
6. у - 4x + 1 = 0
Option 1
• Option 2
Option 3
Option 4
Option 5
Option 6

Answer 1

To find two equations that form a system with no solutions (i.e., they are parallel lines), we need to identify two equations with the same slope but different y-intercepts.

Let's analyze the options:

1. **\(y = 5x - 4\)**: Slope = 5, y-intercept = -4
2. **\(y = -2x + 3\)**: Slope = -2, y-intercept = 3
3. **\(y = 37 + 1\)**: This simplifies to \(y = 38\) (a horizontal line). Slope = 0, y-intercept = 38
4. **\(2y = 6x + 2\)**: Dividing everything by 2 gives \(y = 3x + 1\). Slope = 3, y-intercept = 1
5. **\(y - 5x = 2\)**: Rearranging gives \(y = 5x + 2\). Slope = 5, y-intercept = 2
6. **\(y - 4x + 1 = 0\)**: Rearranging gives \(y = 4x - 1\). Slope = 4, y-intercept = -1

Now, let's summarize the slopes and y-intercepts:
- Option 1: Slope = 5, y-intercept = -4
- Option 2: Slope = -2, y-intercept = 3
- Option 3: Slope = 0, y-intercept = 38
- Option 4: Slope = 3, y-intercept = 1
- Option 5: Slope = 5, y-intercept = 2
- Option 6: Slope = 4, y-intercept = -1

The equations with the same slope (parallel lines) are:
- Option 1: \(y = 5x - 4\) and Option 5: \(y = 5x + 2\)

Since both have a slope of 5 but different y-intercepts (-4 and 2), they are parallel and will have no solutions.

Therefore, the answer is:
**Option 1 and Option 5** form a system with no solutions.