Question

Solve the following systems of equations:
$x-y+z=4$
$x-2y-2z=9$
$2x+y+3z=1$

Answer 1

Subtracting first 2 equations, we get ;

$\Rightarrow y+3z=-5$

$\Rightarrow y=-3z-5$

Substituting $y$ in 3rd equation ;

$\Rightarrow 2x-3z-5+3z=1$

$\Rightarrow x=3$

Substituting $x$ in 1st equation ;

$\Rightarrow y=z-1$

Equating both $y$, we get ;

$\Rightarrow -3z-5=z-1$

$\Rightarrow z=-1$

Substituting $x$ and $z$ in either equation, we get ;

$\Rightarrow y=-2$

$\therefore x=3,y=-2,z=-1$