Two straight line paths are represented by the equations 2x -y = 2 and -4x + 2y = 6 . Then , the paths will

Options

A. Cross each other at one point
B. Not cross each other
C. Cross each other at two points
D. Cross each other at infinitely many points

Answer

To determine the relationship between the two lines represented by the equations \(2x - y = 2\) and \(-4x + 2y = 6\), we will follow these steps:

### Step 1: Rewrite the equations in slope-intercept form (y = mx + b)

1. **For the first equation \(2x - y = 2\)**:
- Rearranging gives:
\[ -y = -2x + 2 \]
- Multiplying through by -1:
\[ y = 2x - 2 \]
- Here, the slope \(m_1 = 2\).

2. **For the second equation \(-4x + 2y = 6\)**:
- Rearranging gives:
\[ 2y = 4x + 6 \]
- Dividing by 2:
\[ y = 2x + 3 \]
- Here, the slope \(m_2 = 2\).

### Step 2: Compare the slopes of the two lines

- We found that:
- \(m_1 = 2\)
- \(m_2 = 2\)

### Step 3: Determine the relationship between the lines

- Since \(m_1 = m_2\), the two lines have the same slope, which means they are parallel.

### Conclusion

- Parallel lines do not intersect or cross each other.

### Final Answer

The paths represented by the equations do not cross each other.

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