Solve the linear equation using the matrices method

Question

Can anyone please help me solve this problem step by step.

6x - y - 9z =5

4x + y -z =6

8x +y - 8z = 8

Answer 1

Answer 2

6 -1 -9 5

4 1 -1 6

8 1 -8 8

-1.5*row2 + row1;

-2*row2 + row3

0 -2.5 -7.5 -4

4 1 -1 6

0 -1 -6 -4

swaps rows; -R1; -R3

4 1 -1 6

0 2.5 7.5 4

0 1 6 4

-2.5*row3 + row2

4 1 -1 6

0 0 -7.5 -6

0 1 6 4

so -7.5 z = -6

7.5 z = 6

z = 6/7.5 = 60/75 =4/5

y + 6z = 4

y + 6(4/5) = 4

y + 24/5 = 4

y = 4 - 24/5

= 20/5 - 24/5

= -4/5

4x + y - z = 6

4x + -4/5 - 4/5 = 6

4x + -8/5 = 6

4x = 6 + 8/5

4x = 30/5 + 8/5

4x = 38/5

x = 38/20 = 19/10