Piece of advice: STAY AWAY from that dude's suggested solution.
4x - 5y + z = 3 ------ eq (i)
2x + y = 4_____y = 4 - 2x ------ eq (ii)
- 7y + 3z = - 5 ------ eq (iii)
- 7(4 - 2x) + 3z = - 5 ------ Substituting 4 - 2x for y in eq (iii)
- 28 + 14x + 3z = - 5
14x + 3z = 23 ----- eq (iv)

4x - 5(4 - 2x) + z = 3 ------ Substituting 4 - 2x for y in eq (i)
4x - 20 + 10x + z = 3
14x + z = 23 ----- eq (v)
2z = 0 ------- Subtracting eq (v) from eq (iv)



- 7y + 3(0) = - 5 ------- Substituting 0 for z in eq (iii)
- 7y = - 5



 ------- Substituting  for y in eq (ii)