How do you solve the system #9x + 9y + z = -112#, #8x + 5y - 9z = -137#, #7x + 4y + 3z = -64#?

1 Answer
Mar 4, 2018

Answer:

#x=-9#, #y=-4# and #z=5#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix

#A=((9,9,1,|,-112),(8,5,-9,|,-137),(7,4,3,|,-64))#

I have written the equations not in the sequence as in the question in order to get #1# as pivot.

Perform the folowing operations on the rows of the matrix

#R2larrR1-R2#; #R3larrR3-R2#

#A=((1,4,10,|,25),(8,5,-9,|,-137),(-1,-1,12,|,73))#

#R2larrR2-8R1#; #R3larrR3+R1#

#A=((1,4,10,|,25),(0,-27,-89,|,-337),(0,3,22,|,98))#

#R2larrR2+9R3#

#A=((1,4,10,|,25),(0,0,109,|,545),(0,3,22,|,98))#

#R2larr(R2)/109#

#A=((1,4,10,|,25),(0,0,1,|,5),(0,3,22,|,98))#

#R1larrR1-10R2#; #R3larrR3-22R2#

#A=((1,4,0,|,-25),(0,0,1,|,5),(0,3,0,|,-12))#

#R3larr(R3)/3#

#A=((1,4,0,|,-25),(0,0,1,|,5),(0,1,0,|,-4))#

#R1larrR1-4R3#

#A=((1,0,0,|,-9),(0,0,1,|,5),(0,1,0,|,-4))#

Thus #x=-9#, #y=-4# and #z=5#