SOLUTION: Determine and Solve a system of equation in three variables & define the variables: The sum of three numbers is none. Two times the first number plus the second number less t

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Question 467075: Determine and Solve a system of equation in three variables & define the variables:
The sum of three numbers is none.
Two times the first number plus the second number less the third number is 30.
Three times the first number subtract four times the second number plus two times the third number is -49?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x+y+z= 0 -------------- 1
2x+y-z= 30 -------------- 2
3x-4y+2z=-49 -------------- 3

consider equation 1 &2 Eliminate y
Multiply 1 by -1 Multiply 2 by 1
we get
-x-y-z= 0
2x+y-z= 30
Add the two
x-2z= 30 ------------- 4
consider equation 2 & 3 Eliminate y
Multiply 2 by -4
Multiply 3 by 1
we get
-8x-4y+4z=-120
3x-4y+2z=-49
Add the two
-5x-8y+6z=-169 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by 5
Multiply (5) by 1
we get
5x-10z= 150
-5x+6z=-169
Add the two
-4z=-19
/-4
z=4.75 OR 4 3/ 4

Plug the value of z in 5
-5x+28.5=-169
-5x=-197.5
x=39.5 OR 39 1/ 2
plug value of x & z in 1
39.5 +y+4.75 = 0
y=-39.5-4.75+0
y= -44.25 OR -44 1/4