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Question
Find the value of k for which the system of equations has a unique solution:
2x + 3y = 5,
kx - 6y = 8
Solution
The given system of equations are
2x + 3y – 5 = 0
kx - 6y - 8 = 0
This system is of the form:
`a_1x+b_1y+c_1 = 0 and a_2x+b_2y+c_2 = 0`
where, `a_1 = 2, b_1= 3, c_1= -5 and a_2 = k, b_2= -6, c_2= -8`
Now, for the given system of equations to have a unique solution, we must have:
`(a_1)/(a_2) ≠ (b_1)/(b_2)`
`⇒ 2/k ≠ 3(−6)`
`⇒ k ≠ -4`
Hence, k ≠ -4
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