What is the solution to this system of linear equations?

2x + y = 1

3x – y = –6

To answer the problem above, it is best to use the elimination method. We can add up the linear equations to eliminate y. This is shown below,
 
                                               2x + y = 1
                                           +  3x - y = -6

This results to, 
                                               5x = -5

which when simplified gives x = -1. 
Substituting this value of x to any of the equation,

                                               2(-1) + y = 1

                                                     y = 3

Thus, the solution to these linear equations is (-1, 3).