In matrix form, the system is given by
I'll use G-J elimination. Consider the augmented matrix
• Multiply through row 1 by -1.
• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.
• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.
• Multiply row 3 by 1/3.
• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.
• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).
Then the solution to the system is
If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix
The third row tells us that . Then in the second row,
and in the first row,