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Question

Find the value for k which each of the following systems of equations has a unique solution:

xky=2,3x+2y+5=0.

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Solution



If a1a2b1b2 then the pair of linear equations a1x+b1y+c1=0,a2x+b2y+c2=0 has a unique solution.

xky2=0 and 3x+2y+5=0

a1=1,b1=k,c1=2

a2=3,b2=2,c2=5

a1a2=13

b1b2=k2

a1a2b1b2


13k2

k23


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