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Question

Write the value of k for which the system of equations 3x2y=0 and kx+5y=0 has infinitely many solutions.

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Solution

The given equations are

3x2y=0

kx+5y=0

For the equations to have an infinite number of solutions, a1a2=b1b2=c1c2

Therefore, a1a2=b1b2

3k=25 [a1a2=3k,b1b2=25]

By cross multiplication, we have

3×5=2×k

15=2k

k=152=152

Hence, the value of k for the system of equation 3x2y=0 and kx2y=0 is 152.


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