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Question

The value of k for which the system of equations x+2y-3=0 and 5x+ky+7=0 has no solution, is


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Solution

Finding the value of k:

First, we compare the given equations with the general equations .

The general equations are a1x+b1y+c1=0 and a2x+b2y+c2=0

After comparing the equations we get a1=1,b1=2,c1=-3 and a2=5,b2=k,c2=7

It is given that the system has no solution it means the system is inconsistent have a set of parallel lines, So a1a2=b1b2c1c2

15=2k-37

15=2k,k=5×2=10

Hence, the value of k is 10.


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