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Question
The condition for the system of linear equations ax + by = c; lx + my = n to have a unique solution is ______.
Options
am ≠ bl
al ≠ bm
al = mb
am = bl
Solution
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
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