Question 626383: Solve the following system of equations. What is the value of y?
x - y - z = 0
3x + y - z = 2
x + 2y + z = 0
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website! x-y-z=0...................(1)
3x+y-z=2...................(2)
x+2y+z=0...................(3)
Multiply (1) by -1 and add to (2)
-x+y+z=0
3x+y-z=2
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2x+2y=2
2(x+y)=2
2(x+y)/2=2/2
x+y=1
x=1-y....................(4)
Add (2) and (3)
3x+y-z=2
x+2y+z=0
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4x+3y=2.................(5)
Put the value of x from (4) to (5)
4(1-y)+3y=2
4-4y+3y=2
4-y=2
-y=2-4
-y=-2
cancel out (-)
y=2
Put the value of y in (4)
x=1-y....................(4)
x=1-2
x=-1
Put the value of x and y in (1)
x-y-z=0...................(1)
-1-2-z=0
-3-z=0
-z=3
z=-3
x,y,z=-1,2,-3
Check
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Put the values of x, y and z in (1)
x-y-z=0...................(1)
-1-2-(-2)=0
-3+3=0
0=0
Put the values of x, y and z in (2)
3x+y-z=2...................(2)
3(-1)+2-(-3)=2
-3+2+3=2
2=2
Put the values of x, y and z in (3)
x+2y+z=0...................(3)
-1+2(2)+(-3)=0
-1+4-3=0
4-4=0
0=0
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