Question

$x+5y+4z=3$ ...(1)
$2x+2y+3z=4$ ...(2)
$4x-2y+z=9$ ...(3)
Find $x,y,z$

Answer 1

$x+5y+4z=3$ .......$\left(1\right)$

$2x+2y+3z=4$ .......$\left(2\right)$

$4x-2y+z=9$ ......$\left(3\right)$

Eqn$\left(2\right)-2\times$Eqn$\left(1\right)$ we get

$\Rightarrow 2x+2y+3x-2x-10y-8z=4-6$

$\Rightarrow -8y-5z=-2$

$\Rightarrow 8y+5z=2$ ........$\left(4\right)$

Eqn$\left(3\right)-4\times$Eqn$\left(1\right)$ we get

$\Rightarrow 4x-2y+z-4x-20y-16z=4-12$

$\Rightarrow -22y-15z=-8$

$\Rightarrow 22y+15z=8$ .........$\left(5\right)$

Eqn$\left(5\right)-3\times$Eqn$\left(4\right)$ we get

$\Rightarrow 22y+15z-24y-15z=8-6$

$\Rightarrow -2y=2$

$\therefore y=-1$

Substitute $y=-1$ in $\left(5\right)$ we get

$22y+15z=8$

$\Rightarrow -22+15z=8$

$\Rightarrow 15z=8+22=30$

$\Rightarrow z=\frac{30}{15}=2$

Substitute $z=2,y=-1$ in $\left(1\right)$ we get

$x+5\times -1+4\times 2=3$

$\Rightarrow x-5+8=3$

$\Rightarrow x+3=3$

$\Rightarrow x=0$

$\therefore x=0,y=-1,z=2$