Slope-Intercept Form
9-12
1
Solving Systems of Equations
Lesson Details
Grade Level
9-12
Duration (minutes)
1
Summary
A Grade 9-12 math lesson teaching students two methods for solving a system of equations — substitution, which replaces a variable with an equal expression, and elimination, which adds or subtracts equations to cancel a variable — each demonstrated with a fully worked example.
Student Worksheet: Solving Systems of Equations
Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!
Key Concepts:
• System of Equations: Two equations that share the same variables, where the solution must make both equations true.
• Substitution: If one equation is already solved for a variable, replace that variable in the other equation with its equal expression.
• Elimination: Add or subtract the two equations so that one variable cancels out, leaving a single-variable equation to solve.
• Finishing the Solution: After finding one variable, substitute it back into either original equation to find the other variable.
Instructions: Read each question carefully and write your answer in the space provided.
- Question 1: In the substitution example, why does 3x + y = 11 become 3x + (2x + 1) = 11?
- Question 2: Solve for x: 5x + 1 = 11. Show your steps.
- Question 3: Using x = 2, find y in the equation y = 2x + 1. What is the full solution to the substitution problem?
- Question 4: In the elimination example, why do the y terms cancel when you add 2x + y = 9 and x – y = 3?
- Question 5: After finding x = 4 in the elimination problem, substitute it into x – y = 3 to find y. What is the full solution?
Click to reveal Teacher Answer Key
1. Because the first equation says y = 2x + 1, so y can be replaced with (2x + 1) in the second equation.
2. Subtract 1 from both sides: 5x = 10. Divide by 5: x = 2.
3. y = 2(2) + 1 = 5. The full solution is x = 2, y = 5.
4. Because one equation has +y and the other has -y, so adding the equations cancels the y terms.
5. 4 – y = 3, so y = 1. The full solution is x = 4, y = 1.
Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.
🎯 Extension Activity: Solve the system y = 3x - 2 and 2x + y = 8 using substitution. Then solve the system x + y = 10 and x - y = 4 using elimination. Show every step for both.