# How do you solve the simultaneous equations #x+y+z=-2#, #2x+5y+2z=-10#, #-x+6y-3z=-16# ?

##### 2 Answers

#### Explanation:

Given:

#{ (x+y+z=-2),(2x+5y+2z=-10),(-x+6y-3z=-16) :}#

Subtracting twice the first equation from the second, we get:

#3y = -6#

Dividing both sides by

#y = -2#

Adding the first and third equation together, we get:

#7y-2z = -18#

Substituting

#-14-2z = -18#

Add

#-2z = -4#

Divide both sides by

#z = 2#

Then putting

#x-color(red)(cancel(color(black)(2)))+color(red)(cancel(color(black)(2)))=-2#

Hence:

#x = -2#

Use the 3 equations to write an Augmented Matrix and then perform elementary row operations until you obtain an identity matrix.

#### Explanation:

Write the augmented matrix:

Perform elementary row operations.

We have obtained an identity matrix and the right column contains the solution set: