SOLUTION: solve this equation. 1. x+y+z=6 2x-y+3z=9 -x+2y+2z=9

Question 515251: solve this equation.
1. x+y+z=6
2x-y+3z=9
-x+2y+2z=9
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
solve this equation.
x+y+z=6.................(1)
2x-y+3z=9...............(2)
-x+2y+2z=9..............(3)

Add (1) and (2)
x+y+z=6.................(1)
-x+2y+2z=9..............(3)
-----------
3y+3z=15
3(y+z)=15
3(y+z)/3=15/3
y+z=5.................(4)
Multiply (3) by 2
-x+2y+2z=9..............(3)
-2x+4y+4z=18
Add above equation and (2)
-2x+4y+4z=18
2x-y+3z=9...............(2)
--------------
3y+7z=27..................(5)
Multiply equation (4) by -3 and add to (5)
-3*(y+z)=-3*5.................(4)
-3y-3z=-15
3y+7z=27..................(5)
------------
4z=12
4z/4=12/4
z=3
Put the value of z in (4)
y+z=5.................(4)
y+3=5
y=5-3
y=2
Put the values of y and z in (1)
x+y+z=6.................(1)
x+2+3=6
x+5=6
x=6-5
x=1
x,y,z = 1,2,3
Check
Put the values of x,y,z in (2)
2x-y+3z=9...............(2)
2(1)-2+3(3)=9
2-2+9=9
9=9
RELATED QUESTIONS
solve the following systems of linear equation in three variables by elimination or... (answered by ReadingBoosters,Edwin McCravy)

x + y + z = 6 2x - y + 3z = 9 -x + 2y +2z =... (answered by midwood_trail)

solve the system x+y+z=-1 x-y+3z=-17 2x+y+z=-2 Solve the system x-y+2z=7... (answered by solver91311)

3x+3y+3z=12 2x+2y+2z=9... (answered by Alan3354)

Solve. If the system's equations are dependent or it there is no solution, state this. (answered by Alan3354)

Solve. If the system's equations are dependent or it there is no solution, state this. (answered by solver91311)

Solve the system: -x-y-2z=9 -2x-2y-z=1... (answered by ikleyn)

x+y+z=6 2x-y+3z=9 -x+2y+2z=9 "please show me step by step using... (answered by elima)

Solve using matrices please x+y+z=9 3x-y+z=-1... (answered by jsmallt9)