Here are five system of equations questions that are suitable for Grade 9 secondary students. These will help reinforce understanding of solving systems of equations using substitution, elimination, and graphical methods.

1. Solving by Substitution

Solve the system of equations:

3x + 2y &= 12 \\ x - y &= 2 \end{aligned}$$ ### 2. **Solving by Elimination** Solve the system of equations using the elimination method: $$\begin{aligned} 4x - 3y &= 7 \\ 2x + 5y &= 13 \end{aligned}$$ ### 3. **Word Problem** The sum of two numbers is 50. One number is 4 less than three times the other. Find the two numbers. Formulate the system and solve it. ### 4. **Graphical Solution** Solve the following system of equations by graphing: $$\begin{aligned} y &= 2x + 1 \\ y &= -x + 4 \end{aligned}$$ What is the point of intersection? ### 5. **Special Case (Infinite Solutions or No Solution)** Solve the system of equations and determine if there are no solutions, exactly one solution, or infinitely many solutions: $$\begin{aligned} 2x + 3y &= 5 \\ 4x + 6y &= 10 \end{aligned}$$ --- Would you like detailed solutions for any of these? Or do you have specific preferences for difficulty or focus? Here are some related questions to deepen the understanding: 1. How can you determine if a system of equations has no solution or infinitely many solutions? 2. What are the differences between the substitution and elimination methods for solving systems? 3. How does the graph of a system of linear equations visually represent solutions? 4. How would you solve systems of equations with three variables (using substitution or elimination)? 5. What real-life scenarios can be modeled using systems of linear equations? **Tip**: Always check if you can simplify the equations (like factoring or dividing) before applying methods, as it can make the problem easier to solve.