x > y > z > 670

x + y + z = 2019

A few possible ways.

1. z = 672, y = 673, x = 674
2. z = 671, y = 672, x = 676
3. z = 671, y = 673, x = 675

One of these should fit the second equation, but I am lazy to evaluate.

Hi student, the steps you should be performing are :

x + y + z = 2019
x = 2019 - y - z

Sub this into 2x + 3y + 4z = 6055,

2(2019 - y - z) + 3y + 4z = 6055
4038 - 2y - 2z + 3y + 4z = 6055
4038 + 2z + y = 6055
y = 6055 - 4038 - 2z
y = 2017 - 2z


Sub this into x = 2019 - y - z,

x = 2019 - (2017 - 2z) - z
x = z + 2


Since x > y > z > 670, and x = z + 2, and given they are all positive integers,

y = z + 1 so that it is in between z and x.

Then 2019 = z + 2 + z + 1 + z

2019 = 3z + 3
2016 = 3z
z = 2016 ÷ 3 = 672

y = 673 and z = 674

Note that the info > 670 is actually not needed as x > y > z , together with them being positive integers and the result x = z + 2 is sufficient to figure out the answer

There is also no need to guess and check