The values of m,n, for which the system of equations gathered x+y+z=4, 2x+5y+5z=17, x+2y+m…

Question

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

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

has infinitely many solutions, satisfy the equation :

Accepted Answer

The given system of linear equations can be represented as,

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

$\because $ System of equations has infinitely many solutions

$	herefore m=2\&n=7$

Which satisfy equation given in option (1).

${2}^{2}+{7}^{2}-14=39$

Solutions · 1