PROBLEM $($BY HAND$)$: Solve the following systems by hand using Gaussian $($or Gauss$-$Jordan$)$ Elimination Algorithm and import the photos of your work.

How many solutions do the systems have?

$x_1-3x_2+7x_3=0$

$-2x_1+x_2-4x_3=0$

$x_1+2x_2+9x_3=0$

$5x_1+8x_2+7x_3=2$

$x_2-x_3=-3$

$x_1+3x_2=2$

$x_1+4x_2-5x_3=0$

$2x_1-x_2+8x_3=9$

$3x_1+5x_2-4x_3+3x_4=2$

$-3x_1-2x_2+4x_3-3x_4=2$

$6x_1+x_2-8x_3+6x_4=-8$