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  • If the system of linear equations <img alt="\mathrm{2 x-3 y=\gamma+5 \text {, }}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%20x-3%20y%3D%5Cgamma&plus;5%20%5Ctext

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

Option: 1

58


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{2 x-3 y=\gamma+5} \\

\mathrm{\alpha x+5 y=\beta+1}

For inifinite solutions, these two lines should co-incide

\mathrm{\frac{2}{\alpha}=\frac{-3}{5}=\frac{\gamma+5}{\beta+1} }\\

\mathrm{\Rightarrow \frac{2}{\alpha}=-\frac{3}{5} \Rightarrow \alpha=-\frac{10}{3} \quad \text { and } }

\mathrm{\frac{\gamma+5}{\beta+1}=\frac{-3}{5}} \\

\mathrm{\Rightarrow 5 \gamma+25=-3 \beta-3} \\

\mathrm{\Rightarrow 3 \beta+5 \gamma=-28 }\\

\mathrm{\therefore |9 \alpha+3 \beta+5 \gamma|=|-30-28 |=58}

Hence answer is 58.

Posted by

Shailly goel

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