The number of values of k for which the system of linear equations,
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :
Solutions · 1
Official solution
System of linear equation have no solution,
\[\therefore\,\,\,\] determinant of coefficient = 0
\[\left| {(k+2k10k+3) } \right| = 0\]
\[ \Rightarrow \] \[\,\,\,\,\] (k + 2) (k + 3) - 10 K = 0
\[ \Rightarrow \] \[\,\,\,\,\] k2 - 5k + 6 = 0
\[\therefore\,\,\,\,\] k = 2, 3
When, k = 2 then equations become,
4x + 10y = 2
and 2x + 5y = 1
It has in finite number of solutions.
When k = 3, equations becomes
5x + 10y = 3
3x + 6y = 2
Those equation has no solutions.
\[\therefore\,\,\,\,\] When k = 3, then system of equations have no solutions.