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 ______

Given system of equations has infinite many solutions a1a2=b1b2=c1c22α=−35=γ+5β+1⇒3α=−10 and −3β−3=5r+253β+5r=−28Now 9α+3β+5r=−30−28=58

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

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 ______

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is 58.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Given system of equations has infinite many solutions $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

$\frac{2}{α} = \frac{- 3}{5} = \frac{γ + 5}{β + 1} \Rightarrow$ $3 α = - 10$ and $- 3 β - 3 = 5 r + 25$

$3 β + 5 r = - 28$

Now $|9 α + 3 β + 5 r| = |- 30 - 28| = 58$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test