IGCSEMaths: CoreCIEExam QuestionsAlgebra & SequencesSimultaneous Equations

Syllabus Edition

First teaching 2023

First exams 2025

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Simultaneous Equations (CIE IGCSE Maths: Core)

Exam Questions

1 hour20 questions
Easy
Medium
Hard
1
Sme Calculator3 marks

Solve the simultaneous equations.
You must show all your working.

table row cell 3 x minus 8 y end cell equals 22 row cell x plus 4 y end cell equals 4 end table

x space equals space...................................... space y space equals space...................................... space

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2a
Sme Calculator2 marks

Esme buys x magazines at $2.45 each and y cards at $3.15 each.

Write down an expression, in terms of x and y, for the total cost, in dollars, of the magazines and the cards.

$ ................................................... 

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2b
Sme Calculator2 marks

Esme spends $60.55 in total.
She buys 8 magazines.

How many cards does she buy?

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3
Sme Calculator3 marks

Solve the simultaneous equations.
You must show all your working.

                  table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x minus y end cell equals 22 row cell x plus 2 y end cell equals 5 end table

x space equals space................................................... space y space equals space................................................... space

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4
Sme Calculator3 marks

Solve the simultaneous equations.

You must show all your working.

5 x minus 2 y space equals space 26 7 x plus 6 y space equals space 10

x equals............................ 

y equals............................ 

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5
Sme Calculator2 marks

Solve the simultaneous equations.
You must show all your working.

table row cell 6 x minus 3 y space end cell equals 12 row cell 2 x space plus space 3 y space end cell equals 16 end table

x space equals ................................. 
y space equals .................................

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1
Sme Calculator4 marks

Solve the simultaneous equations.
You must show all your working.

table row cell 5 x minus 2 y end cell equals 44 row cell 2 x plus 3 y end cell equals 10 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell x space end cell equals cell space................................................. space end cell row cell y space end cell equals cell space................................................. space end cell end table

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2
Sme Calculator4 marks

Solve the simultaneous equations.

You must show all your working.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x plus 4 y end cell equals 10 row cell 7 x minus 6 y end cell equals 43 end table

x space equals space................................................... space y space equals space................................................... space

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3
Sme Calculator3 marks

The equations of two straight lines are y equals 3 x plus 13 and y equals 7 x minus 3.

Use algebra to solve these two simultaneous equations to find the co-ordinates of the point where the lines meet.
You must show all your working.

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4a
Sme Calculator1 mark

A shop sells pens and notebooks.
The cost of a pen is p cents and the cost of a notebook is n cents.

On Monday, the shop sells 5 pens and 4 notebooks for 450 cents.

Complete the equation.

5 p space plus space 4 space n equals..................

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4b
Sme Calculator2 marks

On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents.

Write this information as an equation.

................................................ = .........................

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4c
Sme Calculator3 marks

Solve your two equations to find the cost of a pen and the cost of a notebook.

You must show all your working.

Cost of a pen = ...................................... cents 
Cost of a notebook = ...................................... cents 

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5
Sme Calculator5 marks

Beindu goes to the market to buy apples and bananas.

She can buy

  • 7 apples and 4 bananas for 85 cents

or

  • 3 apples and 8 bananas for 93 cents.

Apples cost a cents each and bananas cost b cents each.

i)
This information can be used to write down two equations.
One of these is 7 a space plus space 4 b space equals space 85.

Write down the other equation.
....................... = ............... [2]
ii)
Solve these two simultaneous equations.
You must show all your working.
a = .................................      
b = .................................  [3]

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1
Sme Calculator5 marks

The Fraser family and the Singh family go to the cinema.
The Fraser family buys 6 adult tickets and 2 child tickets for $124.
The Singh family buys 3 adult tickets and 5 child tickets for $100.

Find the price of an adult ticket and the price of a child ticket.

Adult ticket $ .....................................................
Child ticket $ .................................................

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2
Sme Calculator6 marks

A plant costs p dollars and a bush costs b dollars.
Ana buys 2 plants and 4 bushes for $42.
Paola buys 7 plants and 9 bushes for $107.

Write down a pair of simultaneous equations and solve them to find the value of p and the value of b.
You must show all your working.

p space equals space................................................. space b space equals space................................................. space

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3
Sme Calculator2 marks

Alphonse is x years old and Beatrice is y years old.
Three times Alphonse’s age is equal to 5 times Beatrice’s age.
Twice Beatrice’s age is 4 years more than Alphonse’s age.

i)
Use this information to write down two equations in x and y.
[2]
ii)
Find the age of Alphonse and the age of Beatrice.

                                                                                  Alphonse .................................. years old   

Beatrice .................................. years old [3]

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4
Sme Calculator4 marks

Des thinks of two numbers.
The sum of his two numbers is -6.
The difference between his two numbers is 62.

Find the two numbers.

..................... and .....................

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5
Sme Calculator7 marks

A cost to hire a minibus depends on the number of hours it is hired for, and the number of passengers.
The cost is $h per hour plus $p per passenger.

i)
When the minibus is hired for 3 hours with 10 passengers the cost is $61.

Complete the equation.
3 h plus 10 p equals............................
[1]
 
ii)
When the minibus is hired for 5 hours with 8 passengers the cost is $80.

Write this information as an equation.
[2]
 
iii)
Solve your two simultaneous equations to find h and p.
You must show all your working.
 
h equals................................................       
     
p equals................................................[4]

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