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Question
For what value of k, the following system of equations will represent the coincident lines?
x + 2y + 7 = 0
2x + ky + 14 = 0
Solution
The given system of equations may be written as
x + 2y + 7 = 0
2x + ky + 14 = 0
The given system of equations is of the form
`a_1x + b_1y + c_1 = 0`
`a_2x + b_2y + c_2 = 0`
Where `a_1 = 1, b_1 = 2, c_1 = 7`
And `a_2 = 2,b_2 = k, c_2 = 14`
The given equations will represent coincident lines if they have infinitely many solutions,
The condition for which is
`a_1/a_2 = b_1/b_2 = c_1/c_2 =. 1/2 = 2/k = 7/14 => k = 4`
Hence, the given system of equations will represent coincident lines, if k = 4
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