From here, I know 3 ways to solve. For the elimination method, go here:
2 Unknowns by Elimination Calculator
Enter those 2 equations and press the solve button.
I get (x,y) = (1,1) Plugging those back into the original equations, those work.
You could also use the substitution method here:
2 Unknowns by Substitution Calculator
or Cramer's method here:
2 Unknown Cramer's Method Calculator
Let me know if you have questions.