The pair of linear equations kx + 2y = 5 and 3x + y = 1 has a unique solution if:
Answer & explanation
Correct answer: option 3
The given equations are
kx + 2y = 5
3x + y = 1
We know that,
If (a1/a2) ≠ (b1/b2), then the system of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 has a unique solution.
kx + 2y - 5 = 0 ----(1)
a1 = k, b1 = 2, c1 = -5
3x + y - 1 = 0 ----(2)
a2 = 3, b2 = 1, c2 = -1
According to the question,
(a1/a2) ≠ (b1/b2)
⇒ (k/3) ≠ (2/1)
⇒ 6 ≠ k