1. **Problem:** Solve the system of equations: $$x + y = 10$$ $$x - y = 4$$ **Step 1:** Add the two equations to eliminate $y$. $$(x + y) + (x - y) = 10 + 4$$ $$2x = 14$$ **Step 2:** Solve for $x$. $$x = \frac{14}{2} = 7$$ **Step 3:** Substitute $x = 7$ into the first equation to find $y$. $$7 + y = 10$$ $$y = 10 - 7 = 3$$ **Answer:** The solution to the system is $\boxed{(7, 3)}$. 2. **Problem:** When solving a system by elimination, what is the main goal? **Answer:** The main goal is to *add or subtract the equations to eliminate one variable*. This simplifies the system to one equation with one variable, making it easier to solve.