Question

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 _______.

Answer 1

The correct answer is 58
If 2x – 3y = γ + 5 and αx + 5y = β + 1 have infinitely many solutions
then $\frac{2}{α}=\frac{−3}{5}= \frac{γ+5}{β+1}$
$⇒α=−\frac{10}{3}$
and 3β + 5γ = –28
So |9α + 3β + 5γ|
= |–30 – 28| = 58