Solve the equations: x + y + z = 0 2x + 2y + 2z = 0 -x + 3y + 4z = 2

The set of simultaneous equations to be solved
is:

x + y + z = 0 ...(1)

2x +
2y + 2z = 0 ...(2)

-x + 3y + 4z = 2
...(3)

It can be seen that dividing all the terms of
(2)

2x + 2y + 2z = 0

=>
x + y + z = 0 which is the same as equation (1)

So we have
three variables and 2 equations

We can only express two of
the variables in terms of the third. This gives an infinite number of solutions for the
system.

For example x + y + z =
0

=> x = -y - z

-x + 3y
+ 4z = 2

=> x = 3y + 4z -
2

-y - z = 3y + 4z -
2

=> 4y = -5z +
2

=> y = (-5/4)z +
(1/2)

x = (5/4)z - (1/2) -
z

=> x = (1/4)z -
1/2

The system of equations has infinite
number of solutions.