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Question

Find the value of k for which the given simultaneous equations have infinitely many solutions :
i 4x + y = 7 ; 16x + ky = 28

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Solution

4x + y = 7 16x + ky = 28

Comparing the above equations with the equations a1x + b1y = c1 and a2x+ b2y = c2 , we get:

a1 = 4 b1 = 1 c1 =7a2 = 16 b2 = k c2 = 28a1a2=416 =14; b1b2 =1k and c1c2=728 =14

The condition for simultaneous equations to have infinitely many solutions is
a1a2 = b1b2=c1c214=1k=141k=14k = 4

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