Question 694858: Solve by Elimination. I was told to get rid of z first as a hint and leave as a fraction.
*w+2x+5y=11
-2w+x+4y+2z=-7
w+2x-2y+5z=3
-3w+x=-1
I started out like this: 5(-2w+x+4y+2z=-7)--->-10w+5x+20y+10z=-35
2(w+2x-2y+5z=3) ---> 2w+4x-4y+10z=6
I subtracted because "w" are postive ____________________
-12w+x+24y=-41
the rest I'm still stuck on. Please Show How to solve for x,y,z, and w
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Solve by Elimination. I was told to get rid of z first as a hint and leave as a fraction.
w+2x+5y=11
-2w+x+4y+2z=-7
w+2x-2y+5z=3
-3w+x=-1
I started out like this: 5(-2w+x+4y+2z=-7)--->-10w+5x+20y+10z=-35
2(w+2x-2y+5z=3) ---> 2w+4x-4y+10z=6
I subtracted because "w" are postive ____________________
-12w+x+24y=-41
the rest I'm still stuck on. Please Show How to solve for x,y,z, and w
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z was missing in 2 of the equations, so getting rid of it first makes sense.
Now there are 3 eqns in w, x & y
-------------
w + 2x + 5y = 11
12w-x - 24y = 41
-3w+x = -1
------
Eliminate x since its coefficients are small.
12w-x - 24y = 41
-3w+x = -1
-------------------- Add
9w - 24y = 40 Eqn A
----
1w + 2x + 5y = 11
6w - 2x = 2 ---------------- -3w+x = -1 times -2
---------------- Add
7w + 5y = 13
9w - 24y = 40 Eqn A
--------------
Now it's 2 eqns in x & y
It's a tossup with is next to go
I'll do the y terms
12*(7w + 5y = 13) --> 84w + 120y = 156
5*(9w - 24y = 40) --> 48w - 120y = 200
----
84w + 120y = 156
48w - 120y = 200
--------------------- Add
132w = 356
w = 89/33
-----
Sub into either or the last 2 eqns to find y.
Then sub for w & y to find x
Then sub to find z
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