You write the matrix like this:
| 1 2 |
| 2 3 |
To invert it you use row operations to produce the identity matrix and perform the same row operations on the identity matrix. When you have the identity on the original, you will have the inverse on the identity matrix. Then use matrix multiplication to solve.
The inverse is | -3 2 |
....... | 2 -1 |.
Multiply it by the column vector of the constants to get your answers y=2 and x=-4.