Question

How do you solve this system of equations? x+y+z=-1 2x+4y+z=1 x+2y-3z=-3

Answer 1

x= `2/7`
y=`-4/7`
z=`-5/7`

Explanation:

`x+y+z= -1`
`2x+4y+z= 1`
`x+2y+3z=-3`

If you multiply the third equation by 2, you get:
`2x+4y+6z= -6`

Then you use that subtract second equation, which gives you
`5z = -7`
z = `-5/7`

Now, we kill off z from all the equations we get:
`x+y = -2/7`
`2x+4y = 12/7`
`x+2y = -6/7`

Now just use the third equation and minus the first one, you get:
`y = -4/7`

And plug back in the y and z values into `x+y+z= -1`, you will get:
`x=2/7`