# SOLUTION: I need help with these two matrice problems- solving it by the Gaussian elimination method: problem 1.)2x + y - 3z =1 3x - y + 4z =6

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 Question 116336This question is from textbook college algebra : I need help with these two matrice problems- solving it by the Gaussian elimination method: problem 1.)2x + y - 3z =1 3x - y + 4z =6 x + 2y - z =9 This question is from textbook college algebra Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!I need help with these two matrice problems- solving it by the Gaussian elimination method: problem 1.) ``` 2x + 1y - 3z = 1 3x - 1y + 4z = 6 1x + 2y - 1z = 9 Abbreviate this with an augmented matrix: [2 1 -3 | 1] [3 -1 4 | 6] [1 2 -1 | 9] Get a zero where the 3 is by multiplying the top row by -3, and the middle row by 2: [-6 -3 9 | -3] [ 6 -2 8 | 12] [ 1 2 -1 | 9] Add the top row to the middle row: [-6 -3 9 | -3] [ 0 -5 17 | 9] [ 1 2 -1 | 9] Get a zero where the 1 is by multiplying the top row by 1, and the bottom row by 6: [-6 -3 9 | -3] [ 0 -5 17 | 9] [ 6 12 -6 | 54] Add the top row to the bottom row: [-6 -3 9 | -3] [ 0 -5 17 | 9] [ 0 9 3 | 51] Get a zero where the 9 is on the bottom row by multiplying the middle row by 9, and the bottom row by 5: [-6 -3 9 | -3] [ 0 -45 153 | 81] [ 0 45 15 | 255] Add the middle row to the bottom row: [-6 -3 9 | -3] [ 0 -45 153 | 81] [ 0 0 168 | 336] Rewrite as a new system of equations: -6x - 3y + 9z = -3 -45y + 153z = 81 168z = 336 Solve the bottom equation for z: 168z = 336 z = z = 2 Substitute z = 2 in the middle equation and solve for y: -45y + 153z = 81 -45y + 153(2) = 81 -45y + 306 = 81 -45y = -225 y = y = 5 Substitute y = 5 and z = 2 in the top equation and solve for x: -6x - 3y + 9z = -3 -6x - 3(5) + 9(2) = -3 -6x - 15 + 18 = -3 -6x + 3 = -3 -6x = -6 x = x = 1 So the solution is (x, y, z) = (1, 5, 2) Edwin```