# SOLUTION: Solve the system, if possible x - 4y + z= 9 3y -2z= -7 -x +z= 0 Worked on these problems for over 3 hours and got nowhere. plase help

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Solve the system, if possible x - 4y + z= 9 3y -2z= -7 -x +z= 0 Worked on these problems for over 3 hours and got nowhere. plase help      Log On

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 Algebra: Matrices, determinant, Cramer rule Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Matrices-and-determiminant Question 192037This question is from textbook College Algebra with Modeling and Visualization : Solve the system, if possible x - 4y + z= 9 3y -2z= -7 -x +z= 0 Worked on these problems for over 3 hours and got nowhere. plase helpThis question is from textbook College Algebra with Modeling and Visualization Found 2 solutions by stanbon, ankor@dixie-net.com:Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!x - 4y + z= 9 0 + 3y -2z= -7 -x + 0 +z= 0 -------------------------- Add the 1st row to the 3rd to get: --- x - 4y + z = 9 0 + 3y -2z =-7 0 + -4y +2z= 9 ------------------- Add the 2nd row to the 3rd row to get: x - 4y + z = 9 0 + 3y -2z =-7 0 + -y + 0= 2 -------------------- The 3rd row tells you y = -2 --- Substitute into the 2nd row to solve for "z": 3(-2) - 2z = -7 -6 -2z = -7 -2z = -1 z = 1/2 -------------------------------- Substitute into the 1st row to solve for "x": x - 4y + z = 9 x -4(-2) + (1/2) = 9 x + 8 1/2 = 9 x = 1/2 ================== Cheers, Stan H. Answer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!Solve the system, if possible x - 4y + z= 9 3y -2z= -7 -x +z= 0 ; let's rewrite it and add: x - 4y + z = 9 0x +3y -2z = -7 -x +0y + z = 0 ----------------Addition eliminates x and z -y = 2 y = -2 : Find z using the 2nd original equation 3(-2) - 2z = -7 -6 - 2z = -7 -2z = -7 + 6 -2z = -1 z = z = +.5 ; Find x using the last original equation: -x + .5 = 0 -x = -.5 x = + .5 : Solutions: x=.5; y=-2; z=.5 : Check solution in 1st original equation x - 4y + z = 9 .5 - 4(-2) + .5 = 9 .5 + 8 + .5 = 9