Explanation: answer {x,y,z} = {1,-2,5}
/ Solve equation [3] for the variable x
[3] x = 2y - 5z + 30
// Plug this in for variable x in equation [1]
[1] 2•(2y-5z+30) - 5y + 3z = 27
[1] - y - 7z = -33
// Plug this in for variable x in equation [2]
[2] 4•(2y-5z+30) + 3y - 7z = -37
[2] 11y - 27z = -157
// Solve equation [1] for the variable y
[1] y = -7z + 33
// Plug this in for variable y in equation [2]
[2] 11•(-7z+33) - 27z = -157
[2] - 104z = -520
// Solve equation [2] for the variable z
[2] 104z = 520
[2] z = 5
// By now we know this much :
x = 2y-5z+30
y = -7z+33
z = 5
// Use the z value to solve for y
y = -7(5)+33 = -2
// Use the y and z values to solve for x
x = 2(-2)-5(5)+30 = 1