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Question

Find k for which the system2x+3y-5=0,4x+ky-10=0 has a an infinite number of  solutions.


Solution

2x+3y5=0,
4x+ky10=0

a1=2,b1=3,c1=5a2=4,b2=k,c2=10

 for infinitely many solutions
a1a2=b1b2=c1c2or24=3k
2k=12k=12/2k=6


 

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