Question

Solve the following systems of equations.
$4x-y+4z=0,x+5y-2z=3,-x+8y-2z=1$

Answer 1

Given equations,

$4x-y+4z=0\Rightarrow y=4x+4z$

$x+5y-2z=3$

$\Rightarrow 21x+18z=3$

$7x+6z=1\to \left(1\right)$

$-x+8y-2z=1$

$31x+30z=1\to \left(2\right)$

$5\times \left(1\right)-\left(2\right)$

$4x=4$

$x=1$

$\left(1\right)\Rightarrow 7\left(1\right)+6z=1$

$z=-1$

$y=4(x+z)$

$y=0$

$x=1,y=0,z=-1$ is solution of given equations.