Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve a linear system by substitution
Algebra
CCSS HSA.REI.C.6England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve a linear system by substitution.
- 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: the next skill in this area.
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 (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 + 5 and x + 2y = 31. Find x. → x = 7Prompt: Substitute the first equation into the second.
- Solve: 5x + 4y = 30 and 5x − 4y = 30. Find y. → 0Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
- Solve the system: y = −3x − 2 and 3x + 2y = −22. Find x. → x = 6Prompt: Substitute the first equation into the second.
Hook · 5 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 substitution. 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 the system: y = −3x − 16 4x − 3y = −17 Type the solution like (2, −1).
- Step 1: 4x − 3(−3x − 16) = −17
- Step 2: 13x = −65 → x = −5
- Step 3: y = −1
- Step 4: (−5, −1)
- Answer: (−5, −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 the system: y = −x + 4 −x − 2y = −5 Type the solution like (2, −1). → (3, 1)Prompt: Replace y in the second equation with the first expression.
- Solve the system: x = −y + 3 4x + 5y = 14 Type the solution like (2, −1). → (1, 2)Prompt: x is already on its own: substitute it into the other equation.
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 the system: y = −3x − 9 −x − 4y = 14 Type the solution like (2, −1). → (−2, −3)Prompt: Replace y in the second equation with the first expression.
- To solve y = −4x − 1 and −x + 3y = 2 by substitution, which is the correct next line? (−4x − 1 + 3y = 2 / −x − 3(−4x − 1) = 2 / −x + 3·−4x − 1 = 2 / −x + 3(−4x − 1) = 2) → −x + 3(−4x − 1) = 2Prompt: Substitution replaces y with the whole expression it equals.
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
- 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