Refer to the diagram below. I've marked lines p and r in red, and the angles 3 and 22 in blue. They are corresponding angles because they are both in the same southeast corner of their four-corner configuration.
If the corresponding angles are congruent, then the lines p and r are parallel by the aptly named corresponding angles converse
Get one x+y=3 to y=x+3 and plug it into x-y=1 and you get x-(x+3)=1. Destitute the x and solve. Once you get what x equals plug it to to either equation for the value of x and solve for y