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...
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.`
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