SOLUTION: Hi I am so confused on how to work this because from my understanding, you can get rid of 2 letters when trying to find one. The three I have are 4x+5y+z=23, 2x-5y-z=-11, 3x+y+3z=-

Question 1028392: Hi I am so confused on how to work this because from my understanding, you can get rid of 2 letters when trying to find one. The three I have are 4x+5y+z=23, 2x-5y-z=-11, 3x+y+3z=-5. So far, all i have is x=2. Thank you!
Found 2 solutions by LinnW, ankor@dixie-net.com:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
x = 2 is correct.
Using the first two equations 4x+5y+z=23, 2x-5y-z=-11
If we add the two equations we get
6x = 12
so x =2
We now need two equations to solve for the other two variables.
Let's use 4x+5y+z=23 and 3x+y+3z=-5
If we substitute 2 for x in each, we have
4(2)+5y+z=23 and 3(2)+y+3z=-5
8 + 5y + z = 23 and 6 + y + 3z = -5
Add -8 to each side of the first equation and -6 to each side of the other.
5y + z = 15 and y + 3z = -11
Rewriting
5y + z = 15
y + 3z = -11
Multiply the top equation by -3
-15y - 3z = -45
y + 3z = -11
Adding the two equations we get
-14y = -56
y = 56/14
y = 4
To find z, substitute 4 for y in y + 3z = -11
4 + 3z = -11
add -4 to each side
3z = -15
divide each side by 3
z = -5
We have x = 2 , y = 4 , z = -5
Notice that with the following input to www.wolframalpha.com
4x+5y+z=23; 2x-5y-z=-11; 3x+y+3z=-5 ,
you can obtain the solution.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
4x+5y+z=23,
2x-5y-z=-11,
3x+y+3z=-5.
:
When you know that x = 2, you substitute 2 for x in the equations then
You can choose a pair of equations to find the other variables
using the 2nd and 3rd equations
2(2) - 5y - z -11
4 - 5y -z = -11
-5y - z = -11 - 4
-5y - z = -15
and
3(2) + y +3z = -5
y + 3z = -5 - 6
y + 3z = -11
multiply the 1st equation by 3, add to the above equation
-15y -3z = -45
y + 3z = = -11
---------------
-14y + 0 = -56
y = -56/-14
y = +4
Now substitute 4 for y and find x using either of the two variable equations
-5(4) - z = -15
-20 - z = -15
-z = -15 + 20
-z = 5
z = -5
:
:
Check all three solution in the original equations
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