Solve equation [2] for the variable y
[2] y = 6x + 3z - 12 // Plug this in for variable y in equation [1]
[1] 4x + 3•(6x+3z-12) - z = -6 [1] 22x + 8z = 30 // Plug this in for variable y in equation [3]
[3] 8x + 2•(6x+3z-12) + 4z = 6 [3] 20x + 10z = 30 // Solve equation [3] for the variable z
[3] 10z = -20x + 30 [3] z = -2x + 3// Plug this in for variable z in equation [1]
[1] 22x + 8•(-2x+3) = 30 [1] 6x = 6 // Solve equation [1] for the variable x
[1] 6x = 6 [1] x = 1 // By now we know this much : x = 1 y = 6x+3z-12 z = -2x+3// Use the x value to solve for z
z = -2(1)+3 = 1 // Use the x and z values to solve for y
y = 6(1)+3(1)-12 = -3 Solution : {x,y,z} = {1,-3,1}