Problem solving with simultaneous equations | Maths | Quizalize & Oak National Academy

Starter quiz

Solve using any method: $5x + 4y = 11$ and $2x + 5y = 35$ . Write your answer in the form $(x,y)$ .

'(5, 9)' ✓
Solve using any method: $x + 5y =24$ and $10x + 6y = 20$ . Write your answer in the form $(x,y)$ .

'(-1, 5)' ✓
Solve using any method: $8x + 2y =10$ and $6x - 8y = 36$ . Write your answer in the form $(x,y)$ .

'(2, -3)' ✓
Solve using any method: $12x + 4y = 60$ and $12x - 10y =102$ . Write your answer in the form $(x,y)$ .

'(6, -3)' ✓
Solve using any method: $3x + y = 15$ and $10x - 10y = 90$ . Write your answer in the form $(x,y)$ .

'(6, -3)' ✓
Solve using any method: $3x + 5y = -6$ and $10x - 10y = 60$ . Write your answer in the form $(x,y)$ .

'(3, -3)' ✓

Exit quiz

Which two equations represent this scenario: Nine small bags (s) and five bigger bags (b) contains 182 counters in total. Two small bags and four bigger bags contain 104 counters in total.

$9s + 5b = 104$

$2s + 4b = 182$

$2s + 4b = 104$ ✓

$9s + 5b = 182$ ✓
Which two equations represent this scenario: Five small bags (s) and three bigger bags (b) contains 94 counters in total. Seven small bags and four bigger bags contain 128 counters in total.

$5s + 3b = 7s + 4b$

$5s + 3b = 94$ ✓

$7s + 3b = 94$

$7s + 4b = 128$ ✓
A bakery sells cookies in boxes of small and large sizes. Four small and three large boxes contain 235 cookies. Two small boxes and five large boxes contain 275 cookies. How many are in each box?

Small: 30, Large: 40

Small: 20, Large: 50

Small: 25, Large: 45 ✓
A farmer sells bags of apples and oranges. Three bags of apples and four bags of oranges weigh 73 kg. Five bags of apples and three bags of oranges weigh 85 kg. What is the weight of each bag?

Apples: 9 kg, Oranges: 11 kg

Apples: 11 kg, Oranges: 10 kg ✓

Apples: 10 kg, Oranges: 12 kg
A company produces two types of gadget: standard (s) and premium (p). Selling 5 s and 3 p gadgets makes £260. Selling 3 s and 5 p gadgets makes £220. How much does each type of gadget cost?

Standard: £40, Premium: £20 ✓

Standard: £50, Premium: £20

Standard: £40, Premium: £30
A company produces two types of gadget: standard (s) and premium (p). Selling 6 s and 4 p gadget makes £560. Selling 4 s and 6 p gadgets makes £640. How much does each type of gadget cost?

Standard: £60, Premium: £80

Standard: £40, Premium: £80 ✓

Standard: £80, Premium: £100

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Lesson Details

Key learning points

Where a problem gives multiple ways of connecting two things, it may mean simultaneous equations can be written.
If simultaneous equations can be written, it is important to state what each variable stands for.
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.