SOLUTION: i need help solving this problem :/ solve by using the addition method: 5x + 3y - z = 5 3x - 2y + 4z = 13 4x + 3Y + 5z = 22

Algebra ->  Vectors -> SOLUTION: i need help solving this problem :/ solve by using the addition method: 5x + 3y - z = 5 3x - 2y + 4z = 13 4x + 3Y + 5z = 22      Log On


   

Question 727448: i need help solving this problem :/
solve by using the addition method:
5x + 3y - z = 5
3x - 2y + 4z = 13
4x + 3Y + 5z = 22
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve by using the addition method:
5x + 3y - z = 5
3x - 2y + 4z = 13
4x + 3Y + 5z = 22
:
Multiply the 2nd equation by -1
5x + 3y - z = 5
-3x+ 2y - 4z = -13
4x + 3Y + 5z = 22
--------------------addition eliminates z
6x + 8y = 14
:
multiply the 1st equation by 4, add to the 2nd equation
20x + 12y - 4z = 20
3x - 2y + 4z = 13
------------------addition eliminates z
23x + 10y = 33
:
multiply the 1st two unknowns by -5, multiply the 2nd by 4
-30x + -40y = -70
92x + 40y = 132
--------------------addition eliminates y, find x
62x = 62
x = 1
:
Find y
6x + 8y = 14
6 + 8y = 14
8y = 14 - 6
8y = 8
y = 1
:
Find z
3x - 2y + 4z = 13
3 - 2 + 4z = 13
4z = 13 - 1
4z = 12
z = 12/4
z = 3
:
:
Check the solutions in the 3rd equation
4x + 3Y + 5z = 22
4 + 3 + 5(3) = 22
7 + 15 = 22; confirms our solutions