1. The problem asks to solve a system of equations by factoring and to redo box method problems by filling in the boxes for rows and columns. 2. For factoring, the general approach is to express the equation in a form where you can factor it into products of binomials or polynomials, then set each factor equal to zero to find solutions. 3. For the box method (used in multiplication or factoring), you create a grid where each box corresponds to a product of terms from rows and columns, helping organize terms systematically. 4. Let's illustrate factoring by example: Solve $x^2 + 5x + 6 = 0$ by factoring. 5. Find two numbers that multiply to 6 and add to 5: these are 2 and 3. 6. Rewrite the middle term: $x^2 + 2x + 3x + 6 = 0$. 7. Group terms: $(x^2 + 2x) + (3x + 6) = 0$. 8. Factor each group: $x(x + 2) + 3(x + 2) = 0$. 9. Factor out common binomial: $(x + 3)(x + 2) = 0$. 10. Set each factor to zero: $x + 3 = 0$ or $x + 2 = 0$. 11. Solutions: $x = -3$ or $x = -2$. 12. For the box method, consider multiplying $(x + 2)(x + 3)$: | | x | 2 | |-----|-----|-----| | x | $x^2$ | $2x$ | | 3 | $3x$ | 6 | 13. Sum the terms: $x^2 + 2x + 3x + 6 = x^2 + 5x + 6$. 14. This confirms the factoring and multiplication are consistent. 15. If you provide specific problems from problem 9 or box method examples, I can redo those with detailed steps and filled boxes.