Given :
System of equations :
-5x + 7y + z = 16 ...1)
x + y - 4z = -6 ...2)
-2x -3y -z = -8 ...3)
To Find :
The solution of given system.
Solution :
Putting value of x from equation 2) in equation 1) and 3), we get :
5( -6 + 4z - y ) + 7y + z = 16
21z + 2y = 46 ...4)
-2( -6 + 4z - y ) - 3y - z = -8
12 - 8z + 2y - 3y -z = -8
-9z - y = -20 ...5)
Multiplying equation 5) by 2 and adding equation 4), we get :
3z = 6
z = 2
y = 20 - 18 = 2
Putting value of z and y in equation 2), we get :
x + 2 - 8 = -8
x = -2
Therefore, the solution of the system is ( -2, 2, 2).