Question

The condition for the system of linear equations ax + by = c; lx + my = n to have a unique solution is ______.

पर्याय

• am ≠ bl

• al ≠ bm

• al = mb

• am = bl

Answer 1

The condition for the system of linear equations ax + by = c; lx + my = n to have a unique solution is am ≠ bl.

Explanation:

Given equation

ax + by = c and lx + my = n

Comparing

ax+ by – c = 0 with a₁x + b₁y + c₁ = 0

a₁ = a, b₁ = b, c₁ = –c

Comparing

Ix + my – n = 0 with a₂x + b₂y + c₂ = 0

a₂ = l, b₂ = m, c₂ = –n

∴ For a unique solution

`a_1/a_2 ≠ b_1/b_2`

`\implies a/l ≠ b/m`

`\implies` am ≠ bl