TS ICET 2015 Question Paper with Solutions for online practice

Given : $\mathit{x}-\mathit{y}+\mathit{z}=\mathit{–}6$ ...(i)
$\mathit{x}+\mathit{y}-\mathit{z}=3$...(ii)
$\mathit{–}\mathit{x}+\mathit{y}-\mathit{z}=6$...(iii)
Equations (i) and (iii) are not distinct as one can be obtained from the other on multiplying by (–1),
(i) + (ii) gives,
$2\mathit{x}=\mathit{–}3\Rightarrow \mathit{x}=\frac{-3}{2}$
Now (i) and (ii) reduce to $\mathit{y}-\mathit{z}=6-\frac{3}{2}=\frac{9}{2}$
We can have infinite combinations to satisfy this equation.
Hence, the given set of equations have infinite solutions.
Aliter : Since (i) and (iii) can be obtained from one another, we have only two distinct equations but three unknowns. This will result in infinite solutions for the given system of equations.