IGCSEMathsCambridge (CIE)ExtendedExam QuestionsAlgebra & SequencesSimultaneous Equations

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

Exam code: 0580 & 0980

2 hours28 questions

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Simultaneous Equations

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1
Sme Calculator3 marks

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

1 half x minus 3 y equals 9 space space space 5 x plus y equals 28

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2
Sme Calculator4 marks

Solve the simultaneous equations

     table row cell 2 x space plus space 7 y space end cell equals cell space 17 space end cell row cell 5 x space plus space 3 y space end cell equals cell space – 1 end cell end table

Show clear algebraic working.

table row cell x space end cell equals cell space.................................. end cell row cell y space end cell equals cell space.................................. space end cell end table 

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3
Sme Calculator3 marks

Solve the simultaneous equations

table row cell 5 a space plus space 2 c space end cell equals cell space 10 space end cell row cell 2 a space – space 4 c space end cell equals cell space 7 end cell end table

Show clear algebraic working.

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

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4
Sme Calculator4 marks

Solve the simultaneous equations

table row cell 7 x space – space 2 y space end cell equals cell space 34 space end cell row cell 3 x space plus space 5 y space end cell equals cell space minus 3 end cell end table

Show clear algebraic working.

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

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

How did you do?

1
Sme Calculator6 marks

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

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 7 minus 3 y end cell row cell x squared minus y squared end cell equals 39 end table

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

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2
Sme Calculator4 marks

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

2 x plus 3 y equals negative 12 5 x plus 2 y equals 14  

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

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3
Sme Calculator6 marks

Solve the simultaneous equations       x squared plus y squared equals 9 x plus y equals 2

Give your answers correct to 2 decimal places.

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4
Sme Calculator5 marks

Solve the equations

x squared plus y squared equals 36

x equals 2 y plus 6

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5
Sme Calculator6 marks
A rectangle with a grey horizontal strip in the centre, labelled dimensions: width y, total height 10m, and strip height x.

The diagram above represents a courtyard with a length of y metres and a width of 10 metres.

Mark is designing a rectangular path from one side to another, with a width of xmetres.

The total area of the courtyard, excluding the path, is 116.30 space straight m squared.

A wall is built around the courtyard, along both longer sides and both shorter sides except where the path cuts through. The total length of the wall is 45.52 metres.

Set up and solve a pair of simultaneous equations to find the value of x and the value of y.

Leave your answers to 2 decimal places.

How did you do?

1
Sme Calculator6 marks

The straight line y space equals space 2 x space plus space 1 intersects the curve y space equals space x squared space plus space 3 x space – space 4 at the points A and B.

Find the coordinates of A and B.
Give your answers correct to 2 decimal places.

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

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2
Sme Calculator6 marks

The straight line y space equals space 3 x space plus space 2 intersects the curve y space equals space 2 x to the power of 2 space end exponent plus space 7 x space minus space 11 at two points.
Find the coordinates of these two points.
Give your answers correct to 2 decimal places.

   (....................... , .......................) 

(....................... , .......................) 

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3
Sme Calculator7 marks

The graphs of space y equals open parentheses x minus 1 close parentheses squared space and space y equals fraction numerator 1 space over denominator 2 end fraction x plus 1 space intersect at A and B.   Find the length of AB.  

AB = ................................................

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4
Sme Calculator6 marks

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

table row y equals cell 4 minus x end cell row cell x squared plus 2 y squared end cell equals 67 end table  

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

How did you do?

5
Sme Calculator6 marks

Marco is making patterns with grey and white circular mats.

cie-igcse-2018-may-jun-1-p4-q12

The patterns form a sequence. Marco makes a table to show some information about the patterns.

Pattern number

1

2

3

4

Number of grey mats

6

9

12

15

Total number of mats

6

10

15

21

Marco needs a total of 6 mats to make the first pattern.
He needs a total of 16 mats to make the first two patterns.
He needs a total of 1 over 6 n cubed plus a n squared plus b n mats to make the first n patterns.

Find the value of a and the value of b.

a equals......................................... 
b equals......................................... 

How did you do?