New
New
Year 10
Higher

Problem solving with linear and quadratic simultaneous equations

I can use my knowledge of simultaneous equations to solve problems in context and interpret the solutions.

New
New
Year 10
Higher

Problem solving with linear and quadratic simultaneous equations

I can use my knowledge of simultaneous equations to solve problems in context and interpret the solutions.

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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. The solutions should always be given in context.

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.

Common misconception

Simultaneous equations cannot be applied usefully to real-world scenarios.

The skill of solving a pair of simultaneous equations can be applied to a wide variety of problems and provides us with answers in a wide variety of contexts.

Pupils see a variety of problems in this lesson. Ask pupils to start with their own answers, work backwards, and come up with their own problems to give to each other to solve.
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).

Lesson video

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6 Questions

Q1.
Which equation is true for $$x = 2$$ and $$y = 5$$?
$$2x + y = -8$$
Correct answer: $$3x + 6y = 36$$
$$4x + 2y = 20$$
Q2.
If I add together the pair of simultaneous equations $$7x + 7y = 87$$ and $$5x + 7y = 91$$, what is the resulting equation?
Correct Answer: 12x + 14y = 178, 14y + 12x = 178
Q3.
Multiply this equation by $$5$$: $$3x + 10 = 40$$
Correct Answer: 15x + 50 = 200, 50 + 15x = 200
Q4.
What is the value of $$x$$ for equations $$6x + 8y = 66$$ and $$x + 3y = 16$$?
Correct Answer: 7, x = 7
Q5.
What is the negative coordinate pair that solves both $$x^2 + y^2 = 40$$ and $$x - y = 4$$?
Correct Answer: (-2, -6)
Q6.
What is the negative coordinate pair that solves both $$x^2 + y^2 = 17$$ and $$x - y = 3$$?
Correct Answer: (-1,-4)

6 Questions

Q1.
4 red and 5 blue boxes weigh 33g. 7 red and 2 blue weigh 24g. What is the mass of each box?
Red: 8g, Blue: 6g
Correct answer: Red: 2g, Blue: 5g
Red: 3g, Blue: 4g
Q2.
7 red and 5 blue boxes weigh 86g. 5 red and 7 blue weigh 82g. What is the mass of each box?
Correct answer: Red: 8g, Blue: 6g
Red: 10g, Blue: 8g
Red: 12g, Blue: 4g
Q3.
3 small & 5 large toys cost £185. 5 small & 3 large cost £175. What is the cost of each toy?
Small: £10, Large: £20
Small: £15, Large: £17
Correct answer: Small: £20, Large: £25
Q4.
Using 4 hours of light A and 6 hours of light B consumes 240 watts. If 6 hours of A and 4 hours of B are used instead, it consumes 280 watts. What is the power consumption per hour for each light?
A: 30 watts/hour, B: 20 watts/hour
A: 40 watts/hour, B: 30 watts/hour
Correct answer: A: 36 watts/hour, B: 16 watts/hour
Q5.
A publisher prints novels and textbooks. Printing 4 novels and 6 textbooks costs £320. Printing 6 novels and 4 textbooks costs £280. What is the printing cost for each type of book?
Novel: £30, Textbook: £40
Correct answer: Novel: £20, Textbook: £40
Novel: £40, Textbook: £50
Q6.
A café blends 3 kg of Brazilian beans (B) with 2 kg Columbian (C) to create a blend for £50. Another blend mixes 2 kg from B with 3 kg from C for £60. What is each bean price per kg?
Correct answer: Brazil: £6, Colombia: £16
Brazil: £8, Colombia: £12
Brazil: £9, Colombia: £11