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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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