Question

How do you solve the system of equations algebraically `x-y-z=7, x+2y+3z=-12, 3x-2y+7z=30`?

Answer 1

Multiply the first equation by -3 first. Then go ahead, x=2/26; y=-226/26 and z=46/26

Explanation:

When you multiply the first equation by -3, you will get:
`-3x+3y+3z=-21`
Then combine this equation with the second. Yielding,
`y=9-10z`.

When you see y (in the first (original equation)), write this and for the second original equation do the same.

You will get `x+9z=16` and `x-17z=-30`. You can multiply either the first equation by -1 or the second by -1. You will get
`z=46/26`

Since `y=9-10z`, you can find y now. `y=9-(460/26)` or `y=-226/26`.

Finally, you can easily solve using any original equation. `x=2/26`.