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Question
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n
Solution
The given system of equations may be written as
ax + by − c = 0
lx + my − n = 0
It is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = a, b_1 = b, c_1 = -c`
And `a_2 = l, b_2 = m,c_2 = -n`
For unique solution, we must have
`a_1/a_2 != b_1/b_2`
`=> a/l != b/m`
`=> am != bl`
Hence, `am != bl` is the required condition.
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