CAT 2020 Exam Shift 3 Solved Paper

Question : 54 of 76

Marks: +1, -0

Let

{k}

be a constant. The equations

{kx}+ {y}=3

and

4 {x}+ {ky}=4

have a unique solution if and only if

Solution:

Simultaneous equation have a unique solution only if

\;{a_{1}}/{a_{2}} ≠ \;{b_{1}}/{b_{2}}

From the given equations, a unique solution would exist only if

\;{k}/{2} ≠ \;{2}/{k}

⇒ k^{2} ≠ 4 ⇒|k| ≠ 2

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