How do you solve 5x+2y-z=-7, x-2y+2z=0, and 3y+ z=17?

1 Answer
Aug 4, 2017

The solution is ((x),(y),(z))=((-2),(4),(5))

Explanation:

We perform the Gauss Jordan elimination with the augmented matrix

((1,-2,2,:,0),(5,2,-1,:,-7),(0,3,1,:,17))

R2larrR2-5R1

((1,-2,2,:,0),(0,12,-11,:,-7),(0,3,1,:,17))

R3larr4R3-R2

((1,-2,2,:,0),(0,12,-11,:,-7),(0,0,15,:,75))

R3larrR3/15

((1,-2,2,:,0),(0,12,-11,:,-7),(0,0,1,:,5))

R2larrR2+11R3

((1,-2,2,:,0),(0,12,0,:,48),(0,0,1,:,5))

R2larrR2/12

((1,-2,2,:,0),(0,1,0,:,4),(0,0,1,:,5))

R1larrR1-2R3

((1,-2,0,:,-10),(0,1,0,:,4),(0,0,1,:,5))

R1larrR1+2R2

((1,0,0,:,-2),(0,1,0,:,4),(0,0,1,:,5))