SOLUTION: Hi Tutors: I am working on systems of equations in three variables. I worked up to the point where I solved for Y. I found Y to be -45/119 . I would like some help because working

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi Tutors: I am working on systems of equations in three variables. I worked up to the point where I solved for Y. I found Y to be -45/119 . I would like some help because working      Log On


   

Question 13536: Hi Tutors:
I am working on systems of equations in three variables. I worked up to the point where I solved for Y. I found Y to be -45/119 . I would like some help because working with these kinds of fractions make me real nervous. Please help me? Here is the problem. 2x+y+2z=11 3x+2y+2z=8 x+4y+3z=0 Thank you SAN ANTONIO
Answer by LilSkittleMd(119) About Me  (Show Source):
You can put this solution on YOUR website!
2x+y+2z=11
3x+2y+2z=8
x+4y+3z=0
The first step is to take 2 of the equations, use the elimination method (add the two equations together to eliminate a variable). Use the first and second equation. You have to multiply the first equation by -2 so the y variable will be eliminated.
-4x-2y-4z=-22
3x+2y+2z=8
Now add the two equations together
-x-2z=-14
This is equation number 4. Now you must use either the first and third equation or the second and third equation and eliminate the y variable from them. Use the first and third. You have to multiply the first equation by -4 to have the y variable eliminated.
-8x-4y-8z=-44
x+4y+3z=0
Add the equations
-7x-5z=-44
This is equation number 5. Now you eliminate a variable from equation 4 and 5 to leave you with one variable to solve. Multiply equation 4 by -7 to eliminate the x variable.
-7x-5z=-44
7x+14z=98
9z=54
z=6
Now plug the z value into either equation 4 or 5 to solve for x
-x-2(6)=-14
-x-12=-14
-x=-2
x=2
Now that you have found the x and z variables, take one of the three original equations and plug in x and z variables to find the y variable.
2+4y+3(6)=0
2+4y+18=0
4y+20=0
4y=-20
y=-5
The three values for these equations are:
x is equal to 2
y is equal to -5
z is equal to 6