Question

Solve the following systems of equations.
$x+2y-z=7,2x-y+z=2,3x-5y+2z=-7$

Answer 1

Given equations,

$x+2y-z=7$ $\to \left(1\right)$

$2x-y+z=2$ $\to \left(2\right)$

$3x-5y+2z=-7$ $\to \left(3\right)$

$\left(3\right)+2\times \left(1\right)$ $3x-5y+2z+2x+4y-2z=-7+2\times 7$

$5x-y=7\to \left(4\right)$

$\left(3\right)-2\times \left(2\right)$ $-x-3y=-11$

$x+3y=11\to \left(5\right)$

$3\times \left(4\right)+\left(5\right)$ $15x-3y+x+3y=21+11$

$16x=32$

$x=2$

(5) $\Rightarrow$ $3y=11-x$

$y=3$

(1) $\Rightarrow$ $z=x+2y-7$

$=2+6-7$

$z=1$

$x=2,y=3,z=1$ is solution of given equations.