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JEE Main 202228 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2022 · 28 June · Evening Shift · Mathematics · Determinants

If the system of linear equations 2x - 3y = γ + 5 + 5y = β + 1 ,...

If the system of linear equations
2x−3y=γ+52x - 3y = \gamma + 5
\alphax+5y=β+1\alphax + 5y = \beta + 1, where α,β,γ∈R\alpha, \beta, \gamma \in R has infinitely many solutions, then the value of \left|9\alpha + 3\beta + 5\gamma\right| is equal to

Correct answer

0

Step-by-step solution

Given,

2x−3y=γ+52x - 3y = \gamma + 5

\alphax+5y=β+1\alphax + 5y = \beta + 1

Has infinite many solutions

So, α2=5−3=β+1γ+5\dfrac{\alpha}{2} = \dfrac{5}{- 3} = \dfrac{\beta + 1}{\gamma + 5}

⇒α=−103,5γ+25=−3β−3⇒ \alpha = \dfrac{- 10}{3}, 5\gamma + 25 = - 3\beta - 3

⇒9α=−30,3β+5γ=−28⇒ 9\alpha = - 30, 3\beta + 5\gamma = - 28

Now, 9α+3β+5γ=−589\alpha + 3\beta + 5\gamma = - 58

\left|9\alpha + 3\beta + 5\gamma\right| = 58$

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