Answer
$\{(x,y,z)|y=\frac{7x-2}{4}, z=\frac{-13x+6}{4}\}$
Work Step by Step
1. Multiply 2 to the 1st eqn and add to the 2nd to get $7x-4y=2$
2. Multiply 3 to the 1st eqn and add to the 3rd to get $7x-4y=2$
3. The above two equations are identical, thus we have a dependent system.
4. We have y=\frac{7x-2}{4} and $z=2x-3y=2x-3(\frac{7x-2}{4})=\frac{8x-21x+6}{4}=\frac{-13x+6}{4}$
5. The solution $\{(x,y,z)|y=\frac{7x-2}{4}, z=\frac{-13x+6}{4}\}$ where $x$ is any real number.
