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## Homework Statement

A system of two equations with 3 variables is given.

x + 2y +z = 1

3x - 4y = 2

calculate a thrird equation and add it to the system. the resulting system must have one and only one solution.

## Homework Equations

## The Attempt at a Solution

my guess is that I must solve the matrix

x + 2y +z = 1

3x - 4y = 2

ax + by+ cz =d

for x, y, z but I have no idea how to show that this system has only one solution.

I really need help with this please. Any advice is welcome, thanks in advance.