Suppose a, b, c, and d are real numbers which satisfy the system of equations
a + 2b + 3c + 4d = 10
4a + b + 2c + 3d = 4
3a + 4b + c + 2d = -10
2a + 3b + 4c + d = −4.
Find a + b + c + d.
Add all the equations and we get
10a + 10b + 10c + 10d = 0
So dividing through by 10
a + b + c + d = 0
