If the system of equations : x+y+z=5,\ x+2y+3z=9,\ x+3y+λ z=μ has infinitely many solutions, then the value of λ +μ is :

Mathematics · Determinants

JEE Main 2026 — 4 April, Evening Shift — Question 27

If the system of equations : $x+y+z=5,\ x+2y+3z=9,\ x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda +\mu$ is :

Option A:
16
Option B:
18
Correct
Option C:
19
Option D:
21

Answer: B

Step-by-step solution

$\mathrm{D}=\lambda-5$ $\mathrm{D}_{1}=\lambda+\mu-18$ $\mathrm{D}_{2}=4 \lambda-2 \mu+6$ $\mathrm{D}_{3}=\mu-13$ Here $\mathrm{x}=\frac{\mathrm{D}_{1}}{\mathrm{D}} ; \mathrm{y}=\frac{\mathrm{D}_{2}}{\mathrm{D}} ; \mathrm{z}=\frac{\mathrm{D}_{3}}{\mathrm{D}}$ For infinitely many solutions $\mathrm{D}=\mathrm{D}_{1}=\mathrm{D}_{2}=\mathrm{D}_{3}=0$ $\Rightarrow \lambda=5 ; \mu=13$ $\therefore \lambda+\mu=18$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 4 April, Evening Shift
Subject: Mathematics
Chapter: Determinants
Topic: System of Linear Equations using Determinants