IGCSEMathsCambridge (CIE)ExtendedExam QuestionsAlgebra & SequencesSimultaneous Equations

Simultaneous Equations (Cambridge (CIE) IGCSE Maths: Extended): Exam Questions

Exam code: 0580 & 0980

2 hours31 questions

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Simultaneous Equations

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1
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2 marks

Solve the simultaneous equations.

2 x space plus space y space equals space 7 3 x space minus space y space equals space 8

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

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

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2
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3 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 8 y end cell equals 22 row cell x plus 4 y end cell equals 4 end table

x equals................................................  

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

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3
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3 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 8 y end cell equals 4 row cell 1 half x plus 3 y end cell equals 7 end table   

x = ............................................ 
y = .............................................

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4
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3 marks

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

table row cell 2 x plus 1 half y end cell equals 13 row cell 3 x plus 2 y end cell equals 17 end table

x = ............................................ 
y = ............................................ 

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5
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4 marks

Abdallah buys 3 cucumbers and 5 tomatoes for £14.50.

Emerson buys 5 cucumbers and 4 tomatoes for £15.50.

Work out the cost of a cucumber and the cost of a tomato.

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6
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3 marks

Solve the simultaneous equations.

table row cell 8 x minus 3 y end cell equals 19 row cell 4 x plus 5 y end cell equals 3 end table

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1
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5 marks

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

y space equals space 5 x squared space plus space 4 x space minus space 19 y space equals space 4 x space plus space 1

x = ................... y = ................... 

x = ................... y = ................... 

How did you do?

2
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4 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x plus 5 y end cell equals 27 row cell 5 x minus 3 y end cell equals 44 end table  

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

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3
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5 marks

Solve algebraically the simultaneous equations

x squared plus y squared equals 25 y minus 2 x equals 5

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4a
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1 mark

In this question, all measurements are in centimetres.

Triangle with base x and height h-3 adjacent to a rectangle with width x and height h, both labelled with dimensions.

The height of the triangle is h minus 3 and the height of the rectangle is h.

The length of the base of the triangle and rectangle are both x.

Write down an expression for the area of the triangle.

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4b
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3 marks

The area of the triangle is 15 space cm squared and the area of the rectangle is 42 space cm squared.

Show that x equals 4

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4c
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1 mark

Find the value of h.

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1
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5 marks
cie-igcse-2020-oct-nov-p4-tz1-q5b

The diagram shows a curve with equation y space equals space 2 x to the power of 2 space end exponent minus space 2 x space minus 7.
The straight line with equation y space equals space 3 x space plus space 5 intersects the curve at the points A and B.

Find the coordinates of the points A and B.

A (.................... , ....................)  
B (.................... , ....................) 

How did you do?

2
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5 marks
cie-igcse-2020-oct-nov-p4-tz1-q7

These are the first four diagrams of a sequence.
The diagrams are made from white dots and black dots.

T spaceis the total number of dots used to make all of the first  n diagrams.

T thin space equals space a n to the power of 3 space end exponent plus space b n squared 

Find the value of a and the value of b.
You must show all your working.

a space equals ................................................

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

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3
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5 marks

There are only r red counters and g green counters in a bag.

A counter is taken at random from the bag.

The probability that the counter is green is 3 over 7

The counter is put back in the bag.

2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag. The probability that the counter is green is 6 over 13

Find the number of red counters and the number of green counters that were in the bag originally.

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4
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3 marks

x space colon space y space equals space 7 space colon space 4

x space plus space y space equals space 88

Work out the value of space x space – space y

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5
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6 marks

The prices of two phones are in the ratio x : y.

When the prices are both increased by £20, the ratio becomes 5 : 2.
When the prices are both reduced by £5, the ratio becomes 5 : 1.

Express the ratio x : y in its lowest terms.

How did you do?

6
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6 marks

Solve these simultaneous equations algebraically.

y space space equals space 2 x squared space minus space 7 x space plus space 4

y space equals space 4 x minus space 1

x = ..................... y = .....................
x = ..................... y = .....................

How did you do?