Question

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Answer 1

Sol :

If the a1x+b1Y+ c1 = 0,a2x+b2y+c2 = 0 system has unique solution then

a1/a2 ≠ b1/b2

Given linear equations λx + y = λ2 and x + λy = 1

λ/ 1 ≠ 1 / λ   ⇒ λ2 ≠ 1  ⇒  λ ≠ ±1

∴ λ ≠ ±1 then it has unique solution.

If the a1x+b1Y+ c1 = 0,a2x+b2y+c2 = 0 system has infinitely many solutions then

a1/a2 = b1/b2 = c1/c2.

λ/ 1 = 1 / λ  = λ2 / 1  

∴ λ = ±1 then it has infinitely many solutions.

If the a1x+b1Y+ c1 = 0,a2x+b2y+c2 = 0 system has no solution then

a1/a2 = b1/b2 ≠ c1/c2.

λ/ 1 = 1 / λ  ≠  λ2 / 1  

 λ3 ≠ 1 ⇒ λ ≠ 1

∴ λ = ±1 then it has no solution.

Hope this helps you!!!!