Solve the system of linear equations algebraically.
$\displaystyle x_1 - x_2 + 2x_3 + 2x_4 + 6x_5 = 6$
$\displaystyle 3x_1 - 2x_2 + 4x_3 + 4x_4 + 12x_5 = 14$
$\displaystyle -x_2 - x_3 - x_4 - 3x_5 = -3$
$\displaystyle 2x_1 - 2x_2 + 4x_3 + 5x_4 + 15x_5 = 10$
$\displaystyle 2x_1 - 2x_2 + 4x_3 + 4x_4 + 13x_5 = 13$
I tried to do this many times using various different ways, but I could never get the answer. Help?
I also attached a picture of the original problem for reference.