Question

The following system of equations
$x+y+z=1$
$2x+2y+2z=3$
$3x+3y+3z=4$ has

• A. infinite number of solutions
• B. no solution
• C. unique solution
• D. finitely many solutions
• E. none of these

Answer 1

The correct option is B no solution

$D=\left|\begin{array}{ccc}1& 1& 1\\ 2& 2& 2\\ 3& 3& 3\end{array}\right|=0$
$D_1=0,$ $D_2=0$, $D_3=0$
Let $z=t$
$x+y=1-t$
$2x+2y=3-2t$
Since both the lines are parallel hence no value of x and y
Hence there is no solution of the given equations.