Step 1: Write down the given equations. $$2x - y = 8 \quad \text{(1)}$$ $$3x - y = 17 \quad \text{(2)}$$ Step 2: Isolate $y$ from equation (1). $$2x - y = 8$$ $$-y = 8 - 2x$$ $$y = 2x - 8 \quad \text{(3)}$$ Step 3: Substitute the expression for $y$ from equation (3) into equation (2). $$3x - (2x - 8) = 17$$ $$3x - 2x + 8 = 17$$ $$x + 8 = 17$$ Step 4: Solve for $x$. $$x = 17 - 8$$ $$x = 9$$ Step 5: Substitute the value of $x$ into equation (3) to solve for $y$. $$y = 2(9) - 8$$ $$y = 18 - 8$$ $$y = 10$$ The solution is $x=9$ and $y=10$. $$\boxed{x=9, y=10}$$