Considering 2x+y+z = 2, 4x+2y+2z = 4, x+y+z=3 , which of the following options is true?

To solve this system of equations, we can start by comparing the first and second equations.

The second equation, 4x + 2y + 2z = 4, can be simplified by dividing all terms by 2, resulting in 2x + y + z = 2.

This is exactly the same as the first equation, 2x + y + z = 2.

Therefore, these two equations are not independent and do not provide any new information.

Now, let's compare the first and third equations.

The third equation is x + y + z = 3.

If we subtract the first equation from the third, we get:

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

This simplifies to:

-x = 1

So, x = -1.

Substituting x = -1 into the third equation gives:

-1 + y + z = 3

Solving for y and z gives:

y + z = 4

So, the solution to the system of equations is x = -1, and y + z = 4.

Therefore, the system of equations has infinite solutions, because y and z can be any real numbers that add up to 4.