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Question
Find the value of k for which the system of equations has a unique solution:
x – ky = 2,
3x + 2y + 5=0.
Solution
The given system of equations are
x - ky – 2 = 0
3x + 2y + 5 = 0
This system of equations is of the form:
`a_1x+b_1y+c_1 = 0 and a_2x+b_2y+c_2 = 0`
where,` a_1 = 1, b_1= -k, c_1= -2 and a_2 = 3, b_2 = 2, c_2 = 5`
Now, for the given system of equations to have a unique solution, we must have:
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
⇒ `1/3 ≠ −k/2`
⇒ `k ≠ - 2/3`
Hence, `k ≠ - 2/3`.
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