Find the value of 'k' for which the following system of equation has Infinitely many solution:
Question (1) 2x + 3y - 5 = 0
6x + ky - 15=0
Question (2) 4x + 5y = 3
kx + 15y = 9
Question (3) kx - 2y+6=0
14x- 3y +9=0
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The given system of equations is: 2x + 3y – 5 = 0 6x + ky – 15 = 0 The above equations are of the form a1 x + b1 y − c1 = 0 a2 x + b2 y − c2 = 0 Here, a1 = 2, b1 = 3, c1 = -5 a2 = 6, b2 = k, c2 = -15 So according to the question, For unique solution, the condition is a1a2a1a2 = b1b2b1b2 = c1c2c1c2 26=3k26=3k ⇒ k = 9 Hence, the given system of equations will have infinitely many solutions, if k is 9
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