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Question

For what value of k does the system of equations kx+2y=5,3x4y=10 have

(i) a unique solution,

(ii) no solution?

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Solution

Equations are written as
kx+2y5=03x4y10=0a1=k,b1=2,c1=5a2=3,b2=4,c3=10

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

k324k32

(ii) The pair of linear equations has no solution if a1a2=b1b2c1c2

here,

a1a2=b1b2k3=24k=32


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