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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