What is the solution of the following system?: $x + 9y + z = -12, x + y - 9z = 7, -12x + 4y + z = -4$

Question

2524 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-24T22:04:23

$x=-151/1016,y=-1233/1016,z=-118/127$

We want to solve

${: (color(white)(aaa)x + 9y + z = -12), (color(white)(aaaaaa)x + y - 9z = 7) ,(-12x + 4y + z = -4):}}$

We start by putting the system in echelon form using Gaussian elimination

$1)$ Add $-1$ lots of the 1st equation to the second

${: (color(white)(aaaaa)x + 9y + z = -12), (color(white)(aaaaaaa)-8y - 10z = 19) ,(color(white)(aa)-12x + 4y + z = -4):}}$

$2)$ Add $12$ lots of equation 1 to equation three

${: (color(white)(a)x + 9y + z = -12), (color(white)(aaa)-8y - 10z = 19) ,(112y + 13z= -148):}}$

$3)$ Add 14 lots of equation 2 to equation three

${: (x + 9y + z = -12), (color(white)(aa)-8y - 10z = 19) ,( color(white)(aaaaa)-127z= 118):}}$

We have the system in echelon form, so we now back-substitute.

$z=-118/127$

$y=-1/8(19+10(-118/127))=-1233/1016$

$x=(-12-9(-1233/1016)-(-118/127))=-151/1016$

What is the solution of the following system?: x + 9y + z = -12, x + y - 9z = 7, -12x + 4y + z = -4 x + 9y + z = -12, x + y - 9z = 7, -12x + 4y + z = -4