Problem solving with linear and quadratic simultaneous equations | Maths

Starter quiz

Which equation is true for $x = 2$ and $y = 5$ ?

$2x + y = -8$

$3x + 6y = 36$ ✓

$4x + 2y = 20$
If I add together the pair of simultaneous equations $7x + 7y = 87$ and $5x + 7y = 91$ , what is the resulting equation?

'12x + 14y = 178' ✓
Multiply this equation by $5$ : $3x + 10 = 40$

'15x + 50 = 200' ✓
What is the value of $x$ for equations $6x + 8y = 66$ and $x + 3y = 16$ ?

'7' ✓
What is the negative coordinate pair that solves both $x^2 + y^2 = 40$ and $x - y = 4$ ?

'(-2, -6)' ✓
What is the negative coordinate pair that solves both $x^2 + y^2 = 17$ and $x - y = 3$ ?

'(-1,-4)' ✓

Exit quiz

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

Red: 2g, Blue: 5g ✓

Red: 3g, Blue: 4g
7 red and 5 blue boxes weigh 86g. 5 red and 7 blue weigh 82g. What is the mass of each box?

Red: 8g, Blue: 6g ✓

Red: 10g, Blue: 8g

Red: 12g, Blue: 4g
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

Small: £20, Large: £25 ✓
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

A: 36 watts/hour, B: 16 watts/hour ✓
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

Novel: £20, Textbook: £40 ✓

Novel: £40, Textbook: £50
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?

Brazil: £6, Colombia: £16 ✓

Brazil: £8, Colombia: £12

Brazil: £9, Colombia: £11

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Lesson Details

Key learning points

The features of the equations may mean one method is more preferable for solving.
You can use any of the methods that are valid.
The solutions should always be given in context.

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.

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.