If the system of linear equations 2x-3y=γ+5 αx+5y=β+1, where α,β,γ∈R has infinitely many solutions, then the value of 9α+3β+5γ is equal to

Correct answer: 58. Given, 2x-3y=γ+5 αx+5y=β+1 Has infinite many solutions So, (α)/2=5/(-3)=(β+1)/(γ+5) ⇒α=(-10)/3, 5γ+25=-3β-3 ⇒9α=-30, 3β+5γ=-28 Now, 9α+3β+5γ=-58 9α+3β+5γ=58

Q50 / 90 · JEE Main 2022 (28 Jun Shift 2) · Mathematics

If the system of linear equations
$2 x - 3 y = γ + 5$
$α x + 5 y = β + 1$ , where $α, β, γ \in R$ has infinitely many solutions, then the value of $|9 α + 3 β + 5 γ|$ is equal to

Correct answer: 58

Solution

Given,

$2 x - 3 y = γ + 5$

$α x + 5 y = β + 1$

Has infinite many solutions

So, $\frac{α}{2} = \frac{5}{- 3} = \frac{β + 1}{γ + 5}$

$\Rightarrow α = \frac{- 10}{3}, 5 γ + 25 = - 3 β - 3$

$\Rightarrow 9 α = - 30, 3 β + 5 γ = - 28$

Now, $9 α + 3 β + 5 γ = - 58$

$|9 α + 3 β + 5 γ| = 58$

Hence, the correct answer is 58.

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If the system of linear equations2x-3y=γ+5αx+5y=β+1, where α,β,γ∈R has infinitely many solutions, then the value of 9α+3β+5γ is equal to

Solution

Relevant Questions

If the system of linear equations
$2 x - 3 y = γ + 5$
$α x + 5 y = β + 1$ , where $α, β, γ \in R$ has infinitely many solutions, then the value of $|9 α + 3 β + 5 γ|$ is equal to