Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Solve systems by elimination
Algebra
CCSS 8.EE.C.8.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve systems by elimination.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Check whether a point solves a system
Leads to: Solve real problems with two equations
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Check whether a point solves a system). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is (3, −4) a solution of the system x + 2y = −5 and 3x + 4y = −8? (Yes / No) → NoPrompt: Substitute x and y into BOTH equations.
- Which point solves both x + y = −5 and x − y = −3? ((−5, −3) / (−3, −2) / (−1, −4) / (−4, −1)) → (−4, −1)Prompt: Test each point in both equations.
- Is (5, −3) a solution of the system −4x − 4y = −8 and −4x − 3y = −11? (Yes / No) → YesPrompt: Substitute x and y into BOTH equations.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve systems by elimination. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve: 4x + 3y = 9 and x − 3y = 6. Type the solution like (2, −3).
- Step 1: 5x = 15 → x = 3
- Step 2: 3y = 9 − 12 → y = −1
- Step 3: (3, −1)
- Answer: (3, −1)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Solve: x + 2y = 15 and 2x − 2y = −6. Type the solution like (2, −3). → (3, 6)Prompt: The y-terms are opposites. Add the equations to eliminate y.
- Solve: 4x + 3y = 9 and 8x − y = 53. Type the solution like (2, −3). → (6, −5)Prompt: Multiply the first equation by 2 so the x-terms match.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: 3x + 5y = −4 and 5x − 5y = −20. Type the solution like (2, −3). → (−3, 1)Prompt: The y-terms are opposites. Add the equations to eliminate y.
- Solve: 3x + 3y = 24 and 6x + y = 43. Type the solution like (2, −3). → (7, 1)Prompt: Multiply the first equation by 2 so the x-terms match.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Check whether a point solves a system.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Solve real problems with two equations.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder