Solve the equation x+y+z = 6 2x-y+3z = 9 3x+3y-5z = - 6

[1] z = - x - y + 6

/ / Plug this in for variable z in equation [2]

[2] 2x - y + 3• (-x - y + 6) = 9 [2] - x - 4y = - 9

/ / Plug this in for variable z in equation [3]

[3] 3x + 3y - 5• (-x - y + 6) = - 6 [3] 8x + 8y = 24

/ / Solve equation [2] for the variable x

[2] x = - 4y + 9

/ / Plug this in for variable x in equation [3]

[3] 8• (-4y+9) + 8y = 24 [3] - 24y = - 48

/ / Solve equation [3] for the variable y

[3] 24y = 48 [3] y = 2

/ / By now we know this much:

x = - 4y+9 y = 2 z = - x-y+6

/ / Use the y value to solve for x

x = - 4 (2) + 9 = 1

/ / Use the x and y values to solve for z

z = - (1) - (2) + 6 = 3

Solution : {x, y, z} = {1,2,3}