Solve for three variables, -5x+3y+6z=4, -3x+y+5z=-5, -4x+2y+z=13
Writing out ther three eqns as,
-5x+3y+6z=4 ------------- (1)
-3x+y+5z=-5 ------------- (2)
-4x+2y+z=13 ------------ (3)
Subtracting 3*(2) from (1), and 2*(2) from (3),
-5x - (-9x) + 6z - (15z) = 4 - (-15)
-4x - (-6x) + z - (10z) = 13 - (-10)
Simplifying the above two eqns,
4x - 9z = 19 ------------ (4)
2x - 9z = 23 ------------ (5)
Subtracting (4) from (5),
-2x = 4
x = -2
Substituting for x = -2 into (4),
-8 - 9z = 19
-9z = 27
z = -3
Substituting for x = -2 and z = -3 into (1), i.e. -5x+3y+6z=4,
10 + 3y - 18 = 4
3y = 12
y = 4
Answer: x = -2, y = 4, z = -3