The following systems of equations all have unique solutions. Solve these systems using the method of Gauss-Jordan elimination with matrices.
(a) $x_1 - 2x_2 = -6$
$2x_1 - 3x_2 = -8$
$(x_1, x_2) =
(b) $2x_1 + 2x_2 = 6$
$3x_1 + 2x_2 = 5$
$(x_1, x_2) =
(c) $x_1 + x_3 = 3$
$2x_2 - 2x_3 = -2$
$x_2 - 2x_3 = 6$
$(x_1, x_2, x_3) =
(d) $x_1 + x_2 + 3x_3 = 11$
$x_1 + 2x_2 + 4x_3 = 16$
$2x_1 + x_2 + 6x_3 = 21$
$(x_1, x_2, x_3) =
(e) $x_1 - x_2 + 3x_3 = 5$
$2x_1 - x_2 + 2x_3 = 3$
$3x_1 + x_2 - 2x_3 = 2$
$(x_1, x_2, x_3) =
(f) $-x_1 + x_2 - x_3 = -3$
$3x_1 + x_2 + x_3 = 13$
$4x_1 + 2x_2 + 3x_3 = 18$
$(x_1, x_2, x_3) =