SOLUTION: x-2y+3z=11 4x+2y-3z=4 3x+3y-z=4 Using equations 1 and 2, and 1 and 3, elimiate x first and solve. I can elimiate the x, but once i get to the equation 10y-15z=-40 9y-10z

Algebra ->  Equations -> SOLUTION: x-2y+3z=11 4x+2y-3z=4 3x+3y-z=4 Using equations 1 and 2, and 1 and 3, elimiate x first and solve. I can elimiate the x, but once i get to the equation 10y-15z=-40 9y-10z      Log On


   



Question 715196: x-2y+3z=11
4x+2y-3z=4
3x+3y-z=4
Using equations 1 and 2, and 1 and 3, elimiate x first and solve.
I can elimiate the x, but once i get to the equation
10y-15z=-40
9y-10z=-29
I get stumped. I know the solution is (3,-1,2) But I cannot get it to work. Please help by walking me though it.
Thanks!

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x-2y+3z=11
4x+2y-3z=4
3x+3y-z=4
Using equations 1 and 2, and 1 and 3, elimiate x first and solve.
I can elimiate the x, but once i get to the equation
10y-15z=-40 --> 2y-3z = -8
9y-10z=-29
--------------
2y - 3z = -8 times 9 --> 18y -27z = -72
9y -10z = -29 times 2 -->18y -20z = -58
----
Subtract and you have z.
sub for z, find y
Sub for z & y to find x

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +x+-+2y+%2B+3z+=+11+
(2) +4x+%2B+2y+-+3z+=+4+
(3) +3x+%2B+3y+-+z+=+4+
Add equations (1) and (2)
(1) +x+-+2y+%2B+3z+=+11+
(2) +4x+%2B+2y+-+3z+=+4+
+5x+=+15+
+x+=+3+
Plug this result into both (2) and (3)
(2) +4%2A3+%2B+2y+-+3z+=+4+
(3) +3%2A3+%2B+3y+-+z+=+4+
----------------------
(2) +12+%2B+2y+-+3z+=+4+
(3) +9+%2B+3y+-+z+=+4+
--------------------
(2) +2y+-+3z+=+-8+
(3) +3y+-+z+=+-5+
-----------------
Multiply both sides of (3) by +-3+
and add (2) and (3)
(2) +2y+-+3z+=+-8+
(3) +-9y+%2B+3z+=+15+
+-7y+=+7+
+y+=+-1+
----------
Plug this result into (2) or (3)
(2) +2y+-+3z+=+-8+
(2) +2%2A%28-1%29+-+3z+=+-8+
(2) +-2+-+3z+=+-8+
(2) +-3z+=+-6+
(2) +z+=+2+
--------------
+x+=+3+
+y+=+-1+
+z+=+2+