SOLUTION: Solve the following system of equations. What is the value of y? x - y - z = 0 3x + y - z = 2 x + 2y + z = 0

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: Solve the following system of equations. What is the value of y? x - y - z = 0 3x + y - z = 2 x + 2y + z = 0      Log On

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 Algebra: Expressions involving variables, substitution Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Expressions-with-variables 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 = 0Answer 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 -------------- 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 ------------- 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 ====== 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