JEE Main 2023MathematicsDeterminantsMediumMCQ

JEE Main 2023 — Determinants Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

Let the system of linear equations

x+y+kz=2

2x+3y-z=1

3x+4y+2z=k

have infinitely many solutions. Then the system

k+1 x+2k-1 y=7

2k+1x+k+5y=10 has :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dunique solution satisfying x+y=1

Step-by-step explanation

Linear equations x+y+kz=2, 2x+3y-z=1 and 3x+4y+2z=k have infinitely many solutions.

Therefore,

11k23-1342=0

⇒110-17+k-1=0

⇒10-7-k=0

⇒3-k=0

⇒k=3

For k=3, the second system of equations is

4x+5y=7        …1

7x+8y=10      …2

Clearly, they have a unique solution

Subtracting 1 & 2, we get

3x+3y=3

⇒x+y=1

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About this question

This is a previous-year question from JEE Main 2023, covering the Determinants chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.