magnum wrote:i don't think you can solve these equations without a matrix
x- y- z = 2
3x- 3y+ 2z = 16
2x- y+ z = 9
You could use a matrix, but you can always solve n equations in n unknowns algebraically. In this case, n = 3.
For instance, from the first of these equations, x = 2 + y + z.
Substituting into the second equation:
3(2+y+z) +3y +2z = 16
6 +3y +3z +3y +2z = 16
6 + 6y + 5z = 16
6y + 5z = 10
6y = 10 - 5z
y = 5/3 - (5/6)z
And remember you already have x = 2 + y + z = 2 + [5/3 - (5/6)z] + z = 11/3 + z/6
So, you have x and y both in terms of z, and you can substitute those formulas into the 3rd equation.