You can solve a square system of 2 linear equations using Cramer's Rule or Reduced Row Echelon Form.
A square system has the same number of equations as variables. A square system can be classified as independent, dependent, or inconsistent.
If you have more variables than equations, you would have an underdetermined system and will be classified as dependent or inconsistent.
If you have fewer variables than equations, you would have an overdetermined system and will be classified as independent, dependent, or inconsistent. However in the case of just 2 equations, it cannot be dependent.
Reduced Row Echelon Form (RREF) is solving the system similar to using the elimination method to solve a system of linear equations.
Cramer's Rule is solving the system using determinants. Cramer's Rule is not necessarily faster than RREF, but it doesn't require thinking because it is a formula; this is good for calculators and computers.
Solving with a matrix is usually quicker than solving with variables because there is less to write out. Furthermore, we have other techniques to solve the system over elimination and substitution.
So search for RREF and Cramer's Rule as there are plenty of examples available.