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Question
Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.
Solution
Given linear equations are
x – 3y – 2 = 0 ......(i)
–2x + 6y – 5 = 0 ......(ii)
On comparing with ax + by c = 0, we get
a1 = 1, b1 = –3, c1 = – 2
a2 = –2, b2 = 6, c2 = – 5
`a_1/a_2 = 1/(-2)`
`b_1/b_2 = (-3)/6 = -1/2`
`c_1/c_2 = 2/5`
i.e., `a_1/a_2 = b_1/b_2 ≠ c_1/c_2` ......[Parallel lines]
Hence, two straight paths represented by the given equations never cross each other, because they are parallel to each other.
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