Unique solution condition for linear system

CAT 2020 Slot 3 · Quantitative Ability · Easy · Linear Equations

This is an easy Quantitative Ability question from the CAT 2020 Slot 3 paper. It tests Linear Equations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2020 Slot 3 questions More Linear Equations questions All CAT QA

Let $k$ be a constant. The equations $kx + y = 3$ and $4x + ky = 4$ have a unique solution if and only if

A.
|k| = 2
B.
k \neq 2
C.
|k| \neq 2
D.
k = 2

Answer

Explanation

For a system of linear equations $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$ to have a unique solution: $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ .

Here, $\frac{k}{4} \neq \frac{1}{k} \implies k^2 \neq 4 \implies |k| \neq 2$ .

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace

Unique solution condition for linear system

Explanation

Related Linear Equations questions

Practise this under exam conditions