JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q26

← JEE Main 2022 · 28 Jun · Shift 2

MathematicsInteger+4 / -1Question 26 of 90

If the system of linear equations
$2x-3y=\gamma+5,$
$\alpha x+5y=\beta+1,$
where $\alpha,\beta,\gamma\in\mathbf R$ has infinitely many solutions, then the value of $|9\alpha+3\beta+5\gamma|$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 58

Infinitely many solutions. $\frac\alpha2=\frac5{-3}=\frac{\beta+1}{\gamma+5}$ : $\alpha=-\frac{10}3$ and $3\beta+5\gamma=-28$ .

Value. $|9\alpha+3\beta+5\gamma|=|-30-28|=58$ .

Answer: 58

Topics:Systems of linear equations

← Previous question Next question →

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 26