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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)
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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)
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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)
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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
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