1. Let's create a real-life situation involving algebra. 2. Problem: Suppose you are buying apples and oranges. Apples cost $2 each and oranges cost $3 each. You buy a total of 10 fruits and spend $24. How many apples and oranges did you buy? 3. Formula: Let $x$ be the number of apples and $y$ be the number of oranges. We have two equations: $$x + y = 10$$ $$2x + 3y = 24$$ 4. Step 1: Solve the first equation for $y$: $$y = 10 - x$$ 5. Step 2: Substitute $y$ into the second equation: $$2x + 3(10 - x) = 24$$ 6. Step 3: Simplify: $$2x + 30 - 3x = 24$$ 7. Step 4: Combine like terms: $$\cancel{2x} - 3x + 30 = 24$$ $$-x + 30 = 24$$ 8. Step 5: Subtract 30 from both sides: $$-x + \cancel{30} - 30 = 24 - 30$$ $$-x = -6$$ 9. Step 6: Multiply both sides by $-1$: $$x = 6$$ 10. Step 7: Substitute $x=6$ back into $y = 10 - x$: $$y = 10 - 6 = 4$$ 11. Final answer: You bought 6 apples and 4 oranges.