How to simplify | - 3 4 | ?

Linear equations in three variable:
Step 1. Take any two equation out given three equation, and solve it for one variable.
Take two equations and solve them for the same variable as before.
Now, solve the two equations in this order, find their value, and plug it into any of the three equations.
For example,
$x-2y+3z=9......\left(1\right)-x+3y-z=-6\dots \dots \left(2\right)2x-5y+5z=17.\dots \dots \left(3\right)$
Step 2. Add equation (1) and (2) to eliminate x.
$x-2y+3z+(-x+3y-z)=9–(-6)y+2z=15.....\left(4\right)$
Step 3. Solve, equation 1 and 3, by multiplying equation (1) with -2 and adding to equation (3)
$-2x+4y-6z=-18+(2x-5y+5z=17)=-18+1$
$-y-z=-1\dots ..\left(5\right)$
Step 4. Solve for equation 4 and 5
$y+2z=3-y-z=-1-----------z=2y=-1$
Solve for x, we get $x=1$
Thus, the solution for the given three equations is (1.-1.2)
As a result, we can solve linear equations in three variables in this manner.