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

1 Answer
Mar 4, 2018

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