Solve System 080D03

1. **State the problem:** We need to solve the system of linear equations: $$\begin{cases} 2x + y = 7 \\ x - y = 2 \end{cases}$$ 2. **Formula and rules:** To solve a system of linear equations, we can use substitution or elimination. Here, we'll use substitution. 3. **Isolate a variable:** From the second equation, isolate $x$: $$x = y + 2$$ 4. **Substitute:** Substitute $x = y + 2$ into the first equation: $$2(y + 2) + y = 7$$ 5. **Simplify:** $$2y + 4 + y = 7$$ $$3y + 4 = 7$$ 6. **Solve for $y$:** $$3y = 7 - 4$$ $$3y = 3$$ $$y = \frac{3}{3}$$ $$y = 1$$ 7. **Substitute back to find $x$:** $$x = y + 2 = 1 + 2 = 3$$ 8. **Solution:** The solution to the system is: $$\boxed{(x, y) = (3, 1)}$$