Let Equation 1 be 2x - y = 17 and Equation 2 be x - y = 10. To solve for the equation through elimination, subtract equation 2 from equation 1. This yields an answer of x - 0 = 7. Hence, x = 7. Furthermore, substitute the value of x to any of the equation to solve for y.
2(7) - y = 17 ; y = -3
Therefore, the solution to this system is (7, -3).