Solve the system analytically:
x + y + z = 10
2x + 6y + 2z = 40
-x + 7y - 3z = 26
1. Pick two equation and a letter to eliminate
I will pick equations 1 and 3 and x to eliminate
x + y + z = 10
-x + 7y - 3z = 26
If you just add them as they are, the x's will be
eliminated:
x + y + z = 10
-x + 7y - 3z = 26
-----------------
8y - 2z = 36
2. Pick a different pair of equation and the SAME
letter to eliminate. (You must pick one equation
the same as before but pick the other of them
different
I will pick equations 1 and 2 and eliminate x
x + y + z = 10
2x + 6y + 2z = 40
If you multiply the first through by -2, the x's
will be eliminated when you add them:
-2x - 2y - 2z = -20
2x + 6y + 2z = 40
-------------------
4y = 20
y = 5
3. Solve the system:
8y - 2z = 36
y = 5
Substitute:
8(5) - 2z = 36
40 - 2z = 36
-2z = -4
z = 2
Substitute y = 5 and z = 2 in the
first original equation:
x + y + z = 10
x + 2 + 5 = 10
x + 7 = 10
x = 3
So the solution is (x,y,z) = (3,5,2)
Edwin
