How do you solve linear equations with 3 variables? x+y=4, 2y+z=6, 3x-z=4.

Hello!

The most straightforward method for solving linear system is the substitution method. We express one variable in terms of others from one equation and substitute this expression into all other equations. This way we reduce the number of variables until one remains. Then we go in reverse direction and found the previous variables.

In this specific problem, express `x` from the first equation: `x=4-y.` Then substitute it into the second and third equations:

`2y+z=6` and `3(4-y)-z=4,` or `3y+z=8.`

Now express `z=6-2y` and substitute, `3y+(6-2y)=8,` or `y=2.`

No go back, recall that `z=6-2y=2,` and back, `x=4-y=2.`

So the answer is x=2, y=2, z=2.