SOLUTION: Please solve for X, Y, and Z in the 3 variable equation. x + 2y + z =6 x + y =4 3x + y + z =8

Question 2157: Please solve for X, Y, and Z in the 3 variable equation.
x + 2y + z =6
x + y =4
3x + y + z =8

Found 2 solutions by matthew_sessoms, gsmani_iyer:
Answer by matthew_sessoms(39) (Show Source): You can put this solution on YOUR website!
Lets number each equation so we can refer to each one with only a number (instead of writing the whole equation).

1) x + 2y + z = 6
2) x + y = 4
3) 3x + y + z = 8

Now lets eliminate 1 (one) variable from from all the equations. Lets start with only 2 equations at a time. I will eliminate x from #1 & #2 first.

(-1) * #1 = -x - 2y - z = -6
#2 = x + y = 4
-------------------

Then add these, and we will get equation #4, like this
#4 = -y - z = -2

Now, lets eliminate the SAME variable (x) from equation #1 & #3 (since before, we eliminated x from #1 & #2)

(-3) * #1 = -3x - 6y - 3z = -18
#3 = 3x + y + z = 8
---------------------

Add these, and we get equation #5, which is
#5 = -5y - 2z = -10

All we have now is 2 equations with 2 variables (#4 & #5). We can use "substitution to solve for y in #4 and plug it in #5.

#4 = y = 2 - z

Now plug in #4, which we solved for y, into #5 and simplify.

-5(2 - z) - 2z = -10
z = 0

Now, plug in z=0 in either #4 or #5. I chosed #4 because it looks easier.

-y - 0 = -2
y = 2

Now, since we have y & z, we can plug these values into either of the original equations (#1, #2, or #3). I chosed #1 because it looks easier.

x + 2(2) + 0 = 6
x = 2

Now we have our final answer, (2, 2, 0), as in (x, y, z).

CHECK
#1. 2 + 2(2) + 0 = 6
#2. 2 + 2 = 4
#3. 3(2) + 2 + 0 = 8
MS
Answer by gsmani_iyer(201) (Show Source): You can put this solution on YOUR website!
X + 2Y + Z = 6 .............(1)
3X + Y + Z = 8 .............(2)
X + Y = 4 .............(3)
Subtracting Eq.(2) from Eq.(1), we get
-2X + Y = -2 .............(4)
(3)-(4), we get
3X = 6
So, X = 2
and Y = 2 (By replacing the values of X an Y in Eq.3)
By replacing these values in Eq. No.2,
= 3*2 + 2 + Z = 8
= 8 + Z = 8
= Z = 0
So, X=2; Y=2; Z=0

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