2x+3y+5z=11 x-y+z=1 3x-4y-5z=10
This is a set of 3 simultaneous equations, which can be solved by elimination/substitution.
2x+3y+5z=11 --------------- (1)
x-y+z=1 ---------------------- (2)
3x-4y-5z=10 ---------------- (3)
Eliminate x from the three eqns by substituting x = 1 + y - z, from (2), into (1) and (3).
This gives us,
5y + 3z = 9 ---------------- (4)
y + 8z = -7 ----------------- (5)
Now eliminate y from the last two eqns by substituting y = -8z - 7, from (5), into (4).
This gives us,
33 + 37z = -11
37z = -44
z = -44/37
This also gives x = 174/37 and y = 93/37
Answer: x = 174/37, y = 93/37, z = -44/37