How do you solve the system #5x + 5y - 6z = -21#, #-2x + y - 3z = -18#, #-x +6y - 6z = -25#?

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Answer 1 · 2017-07-30T06:24:22

The solution is #((x),(y),(z))=((1),(2),(6))#

We perform the Gauss Jordan elimination with the augmented matrix

#((5,5,-6,:,-21),(-2,1,-3,:,-18),(-1,6,-6,:,-25))#

#R1larr-R3# and #R3larrR1#

#((1,-6,6,:,25),(-2,1,-3,:,-18),(5,5,-6,:,-21))#

#R3larr2R3+5R2#

#((1,-6,6,:,25),(-2,1,-3,:,-18),(0,15,-27,:,-132))#

#R2larrR2+2R1#

#((1,-6,6,:,25),(0,-11,9,:,32),(0,15,-27,:,-132))#

#R3larr11R3-15R2#

#((1,-6,6,:,25),(0,-11,9,:,32),(0,0,-162,:,-972))#

#R3larr(R3)/(-162)#

#((1,-6,6,:,25),(0,-11,9,:,32),(0,0,1,:,6))#

#R2larrR2-9R3#

#((1,-6,6,:,25),(0,-11,0,:,-22),(0,0,1,:,6))#

#R2larr(R2)/(-11)#

#((1,-6,6,:,25),(0,1,0,:,2),(0,0,1,:,6))#

#R1larrR1+6R2-6R3#

#((1,0,0,:,1),(0,1,0,:,2),(0,0,1,:,6))#