New
New
Year 10
Foundation

Solving simultaneous equations via any method

I can determine which method of solving is most appropriate and interpret the solutions (in context).

New
New
Year 10
Foundation

Solving simultaneous equations via any method

I can determine which method of solving is most appropriate and interpret the solutions (in context).

Lesson details

Key learning points

  1. The features of the equations may mean one method is more preferable for solving.
  2. You can use any of the methods that are valid.
  3. You can use the other methods to check your solution.
  4. The solution should be interpreted in context if context was stated.

Common misconception

One method is superior when solving simultaneous equations.

Understanding that there are often multiple ways to solve the same problem and then be able to accurately execute a variety of methods is very useful. In this topic, it can enable pupils to confirm their solutions.

Keywords

  • Substitution - Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.

  • Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.

A good challenge is to ask pupils to solve the same pair of linear equations using three or more methods. This is an opportunity for them to practice their fluency and also to acknowledge that they have the capacity to check and confirm their own answers.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 32$$ and $$3x + 9y = 51$$?
Correct Answer: 2, x = 2
Q2.
Using substitution, what is the value of $$x$$ for simultaneous equations $$7x + 2y = 36$$ and $$4x + 2y = 30$$?
Correct Answer: 2, x = 2
Q3.
Using substitution, what is the value of $$y$$ for simultaneous equations $$y - x = -1$$ and $$3x + y = 19$$?
Correct Answer: 4, y = 4
Q4.
Which multiplier would match the x coefficients for equations 1) $$6x + 10y = 42$$ and 2) $$x + 2y = 8$$:
multiply equation 1) by 2
multiply equation 1) by 3
Correct answer: multiply equation 2) by 6
multiply equation 2) by 5
Q5.
What is the value of $$y$$ for simultaneous equations $$x + 4y = 7$$ and $$2x + 3y = -1$$
Correct Answer: 3, y = 3
Q6.
What is the value of $$x$$ for simultaneous equations $$x + y = 7$$ and $$6x + 3y = 27$$
Correct Answer: 2, x = 2

6 Questions

Q1.
Solve using any method: $$3x + 5y = -6$$ and $$5x - 5y = 30$$. Write your answer in the form $$(x,y)$$.
Correct Answer: (3, -3)
Q2.
Solve using any method: $$3x + y = 15$$ and $$5x - 5y = 45$$. Write your answer in the form $$(x,y$$).
Correct Answer: (6, -3)
Q3.
Solve using any method: $$6x + 2y = 30$$ and $$6x - 5y = 51$$. Write your answer in the form $$(x,y)$$.
Correct Answer: (6, -3)
Q4.
Solve using any method: $$8x + 2y =10$$ and $$3x - 4y = 18$$. Write your answer in the form $$(x,y)$$.
Correct Answer: (2, -3)
Q5.
Solve using any method: $$x + 5y =24$$ and $$5x + 3y = 10$$. Write your answer in the form $$(x,y)$$.
Correct Answer: (-1, 5)
Q6.
Solve using any method: $$5x + 4y = 11$$ and $$2x + 5y = 35$$. Write your answer in the form $$(x,y)$$.
Correct Answer: (-5, 9)