QJEEM24Mac9be: JEE Main 2024 Mathematics - Class 12 JEEM24Mac9be Solution: The values of m , n , for which the system of equations x + y + …

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QJEEM24Mac9be: JEE Main 2024 Mathematics - Class 12 JEEM24Mac9be Solution: The values of m , n , for which the system of equations x + y + …

The values of $m, n$ , for which the system of equations

$\begin{aligned} x + y + z = 4, \\ 2 x + 5 y + 5 z = 17, \\ x + 2 y + m z = n \end{aligned}$

has infinitely many solutions, satisfy the equation :

Multiple Choice Options

A m2+n2−m−n=46
B m2+n2+mn=68
C m2+n2−mn=39
D m2+n2+m+n=64

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Accepted Answer

The given system of linear equations can be represented as,

$\begin{aligned} (\begin{array}{cccc} 1 & 1 & 1 & 4 \\ 2 & 5 & 5 & 17 \\ 1 & 2 & m & n \end{array}) \\ \sim (\begin{array}{cccc} 1 & 1 & 1 & 4 \\ 0 & 3 & 3 & 9 \\ 0 & 1 & m - 1 & n - 4 \end{array}) \\ \sim (\begin{array}{cccc} 1 & 1 & 1 & 4 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & m - 2 & n - 7 \end{array}) \end{aligned}$

$∵$ System of equations has infinitely many solutions

$∴ m = 2 & n = 7$

Which satisfy equation given in option (1).

$(i.e., 2^{2} + 7^{2} - 14 = 39)$

QJEEM24Mac9be: JEE Main 2024 Mathematics - Class 12 JEEM24Mac9be Solution: The values of m , n , for which the system of equations x + y + …

Multiple Choice Options

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