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:
Pair of linear equations given are
x - 3y = 2 ------------------- (1)
-2x + 6y = 5 ---------------- (2)
Comparing both the equations with the general form of a straight line, ax + by + c = 0, we get,
a₁ = 1, a₂ = -2,
b₁ = -3, b₂ = 6,
c₁ = -2. c₂ =- 5.
On dividing the equations, we get,
a₁/a₂ = - 1/2
b₁/b₂ = - 3/6 = - 1/2
c₁/c₂ = 2/5.
a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
Hence,they are parallel lines.
Therefore, two straight paths represented by the given equations never cross each other. They are parallel to each other
✦ Try This: Two straight paths are represented by the equations x - y = 1 and -3x + 7y = 6. Check whether the paths cross each other or not
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 5
Two straight paths are represented by the equations x - 3y = 2 and -2x + 6y = 5. Check whether the paths cross each other or not
Summary:
Two straight paths represented by the equations x - 3y = 2 and -2x + 6y = 5 never cross each other.
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