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Question
For what value of , the following system of equations will be inconsistent?
4x + 6y - 11 = 0
2x + ky - 7 = 0
Solution
The given system of equation may be written as
4x + 6y - 11 = 0
2x + ky - 7 = 0
The system of equation is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = 4, b_1 = 6, c_1 = -11`
And `a_2 = 2, b_2 = k, c_2 = -7`
For a unique solution, we must have
`a_1/a_2 = b_1/b_2 != c_1/c_2`
Now
`a_1/a_2 = b_1/b_2`
`=> 4/2 = 6/k`
`=> 4k = 12`
`=> k = 12/4 = 3`
Clearly, for this value of k, we have
`a_1/a_2 = b_1/b_2 != c_1/c_2
Hence, the given system of equation is inconsistent, when k = 3
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