Line up the equations like this:
2u - 3v = 13
3v + w = -3
4u - w = 2
Eliminate w by adding the second and 3rd equations:
3v + w = -3
4u - w = 2
-----------------
4u + 3v = -1
Solve the system consisting of this equation
and the first original equation:
4u + 3v = -1
2u - 3v = 13
Eliminate v by adding these equations:
4u + 3v = -1
2u - 3v = 13
------------
6u = 12
u = 2
Substitute that in
2u - 3v = 13
2(2) - 3v = 13
4 - 3v = 13
-3v = 9
v = -3
Substitute that in
3v + w = -3
3(-3) + w = -3
-9 + w = -3
w = 6
(u, v, w) = (2, -3, 6)
Edwin
