Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Solve a linear system by adding or subtracting equations
Algebra
CCSS HSA.REI.C.5CCSS HSA.REI.C.6England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve a linear system by adding or subtracting equations.
- 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: Systems of linear equations (simultaneous equations)
Leads to: Solve a linear system by scaling equations before eliminating
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Systems of linear equations (simultaneous equations)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = x and x + y = 16. Find x. → x = 8Prompt: Substitute the first equation into the second.
- Solve: 5x + y = 21 and 5x − y = 9. Find y. → 6Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
- Solve the system: y = 3x − 5 and 2x + y = −20. Find x. → x = -3Prompt: Substitute the first equation into the second.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve a linear system by adding or subtracting equations. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve: −5x + y = −15 4x − y = 13 Type the solution like (2, −1).
- Step 1: −x = −2 → x = 2
- Step 2: y = −5
- Step 3: (2, −5)
- Answer: (2, −5)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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: 3x + 3y = −30 −5x − 3y = 40 Type the solution like (2, −1). → (−5, −5)Prompt: The y terms are opposites. What happens if you add the equations?
- Which first move eliminates y straight away? x + 4y = 2 5x + 7y = 2 (Add the equations / Subtract the equations / Multiply one equation first) → Multiply one equation firstPrompt: Look only at the y coefficients.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: 5x − 3y = 18 5x − y = 6 Type the solution like (2, −1). → (0, −6)Prompt: Both equations have the same x term.
- Which first move eliminates y straight away? 4x + 5y = −2 x − 5y = 6 (Add the equations / Subtract the equations / Multiply one equation first) → Add the equationsPrompt: Look only at the y coefficients.
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: Systems of linear equations (simultaneous equations).
- 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 a linear system by scaling equations before eliminating.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder