Question 936830: This is a 3 variable linear equation problem, that I am not sure how to combine to solve. The problem is to solve the system using linear combination method. Here are the three equations:
5x-4y+4z=18
-x+3y-2z=0
4x-2y+7z=3
I have combined the first and second problem to eliminate z, but I don't know what to do from there.
First I distibuted a scale of 2 to the second problem so that the z's would cancel out, and then I solved.
(2)-x+3y-2z=0
-2x+6y-4z=0
5x-4y+4z=18
+ -2x+6y-4z=0
__________________
3x+2y =18
Please help me eliminate another variable so I can solve the rest of the problem.
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 5 x -4 y + 4 z = 18 -------------- 1
-1 x + 3 y -2 z = 0 -------------- 2
4 x -2 y + 7 z = -3 -------------- 3
consider equation 1 &2 Eliminate y
Multiply 1 by 3 -5
Multiply 2 by 4 4
we get
15 x -12 y + 12 z = 54
-4 x + 12 y -8 z = 0
Add the two
11 x 0 y + 4 z = 54 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by 2
Multiply 3 by 3
we get
-2 x + 6 y -4 z = 0
12 x -6 y + 21 z = -9
Add the two
10 x + 0 y + 17 z = -9 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by -10
Multiply (5) by 11
we get
-110 x -40 z = -540
110 x + 187 z = -99
Add the two
0 x + 147 z = -639
/ 147
z = -4 17/49
10 x + 17 z= -9
10 x -73 44/49 = -9
x = 6 24/49
Plug x & z in eq (1)
5 x -4 y + 4 z = 18 -------------- 1
32 22/49 -4 y -17 19/49 = 18
-4 y = 2 46/49
y = - 36/49
x= 6 24/49 y= - 36/49 z= -4 17/49
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
This is a 3 variable linear equation problem, that I am not sure how to combine to solve. The problem is to solve the system using linear combination method. Here are the three equations:
5x-4y+4z=18
-x+3y-2z=0
4x-2y+7z=3
I have combined the first and second problem to eliminate z, but I don't know what to do from there.
First I distibuted a scale of 2 to the second problem so that the z's would cancel out, and then I solved.
(2)-x+3y-2z=0
-2x+6y-4z=0
5x-4y+4z=18
+ -2x+6y-4z=0
__________________
3x+2y =18
Please help me eliminate another variable so I can solve the rest of the problem.
The easiest variable to eliminate is x. You do this by MULTIPLYING equation 2 by 5 to create equation (iv).
Then subtract equation (iv) from equation (i). You now have an equation in 2 unknowns (y and z). This is equation (v)
You then MULTIPLY equation 2 by 4 to create equation (vi). Then subtract equation (vi) from equation (iii).
You now have an equation in 2 unknowns (y and z). This is equation (vii)
Eliminate one of the variables from equations (v) and (vii). When you have 1 equation in 1 unknown,
and solve for that unknown, you will then be able to determine the values for the other 2 variables.
When all is "said and done," you should obtain: 
You can do the check!!
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