1. **Problem:** Solve the system of equations: $$2x + 3y = 7$$ $$x = 4 - y$$ 2. **Formula:** To solve a system of equations, substitute one equation into the other or use elimination. 3. **Step 1:** Substitute $x = 4 - y$ into the first equation: $$2(4 - y) + 3y = 7$$ 4. **Step 2:** Simplify and solve for $y$: $$8 - 2y + 3y = 7$$ $$8 + y = 7$$ $$y = 7 - 8$$ $$y = -1$$ 5. **Step 3:** Substitute $y = -1$ back into $x = 4 - y$: $$x = 4 - (-1) = 4 + 1 = 5$$ 6. **Final answer:** The solution to the system is $x = 5$, $y = -1$.