what is gaussian elimination method

Question

Use the Gaussian elimination method to solve the system of linear equations. If the system has infinitely many​ solutions, write the solution set with z arbitrary.

x + 2y + 2z =2

-x + 3y + 5z =1

x + y = -13

Answer 1

Gaussian elimination works like this:

You set up the augmented matrix representing the system of equations:

Add the first row to the second to obtain

Add −1 times the first row to the third to obtain

Multiply the second row by ⅕ to obtain

The next step is to add the second row to the third row...

And you continue doing row operations (like the ones shown above) until your first three columns form a diagonal matrix and the last column contains the solutions for each of the three variables:

which means x = a, y= b, and z = c