#7x - 3y - 2z = 0# => eq-1
#4x - 4y - z = 2# => eq-2
#5x + 2y + 3z = 1# => eq-3
Eliminate z between 1 & 2, multiply eq-2 by -2:
#7x - 3y - 2z = 0#
#-8x + 8y + 2z = -4# => add the 2 equations:
#-x + 5y = -4# => eq-4
Eliminate z between 2 & 3, multiply eq-2 by 3:
#12x - 12y - 3z = 6#
#5x + 2y + 3z = 1# => add the 2 equations:
#17x - 10y = 7# => eq-5
Eliminate y between 4 & 5, multiply eq-4 by 2:
#-2x + 10y = -8#
#17x - 10y = 7# => add the 2 equations, y's cancel solve for x:
#15x = -1#
#x = -1/15#
Substitute for x in eq-4, solve for y:
#-(-1/15) + 5y = -4#
#5y = -4 - 1/15#
#5y = -61/15#
#y = -61/75#
Substitute for x and y in eq-2 solve for z:
#4(-1/15) - 4(-61/75) - 2 = z#
#z = 244/75 - 4/15 - 2#
#z = (244 - 20 - 150)/75#
#z = 74/75#
Thus:
#(x, y, z) = (-1/15, -61/75, 74/75)#
