You may use the substitution method to solve the system, hence, you need to use the first equation to write x in terms of z, such that:

`2x + 2z = 2 => x + z = 1 => x = 1 - z`

You may now replace 1 - z for x in equation `5x + 3y = 4,` such that:

`5(1 - z) + 3y = 4 =>5 - 5z + 3y = 4 => - 5z + 3y = -1`

You may use the third equation, `3y - 4z = 4` , along with `-5z + 3y = -1 ` equation, such that:

`3y = 4 + 4z`

Replace 4 + 4z for 3y in equation -5z + 3y = -1, such that:

`-5z + 4 + 4z = -1 => -z = -1 - 4 => -z = -5 => z = 5`

You may replace 5 for z in equation `3y = 4 + 4z:`

`3y = 4 + 4*5 => 3y = 24 => y = 8`

You may replace 5 for z in equation `x = 1 - z:`

`x = 1 - 5 => x = -4`

**Hence, evaluating the solution to the given system, yields **`x = -4, y = 8, z = 5.`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now