[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}
