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Question
Find the value of k for which the system 3x+5y=0,kx+10y=0 has a nonzero solution.
Find the value of k for which the system 3x+5y=0,kx+10y=0 has a nonzero solution.
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Solution
3x+5y=0
kx+10y=0
condition for the system of equations to have non-zero solutions,
a1/a2 = b1/b2 = c1/c2
here, a1 = 3 , a2 = k, b1 = 5 , b2 = 10
3/k = 5/10
3/k = 1/2
k = 6
kx+10y=0
condition for the system of equations to have non-zero solutions,
a1/a2 = b1/b2 = c1/c2
here, a1 = 3 , a2 = k, b1 = 5 , b2 = 10
3/k = 5/10
3/k = 1/2
k = 6
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