O LevelMathsCambridgeTopic QuestionsAlgebra & SequencesSimultaneous Equations

Simultaneous Equations (Cambridge O Level Maths)

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1
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 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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2
Sme Calculator3 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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1
Sme Calculator2 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
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 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
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 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
Sme Calculator3 marks

Solve the simultaneous equations.
Show your working.

table row cell x plus 6 y end cell equals 0 row cell 3 x minus 2 y end cell equals 10 end table

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

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1
Sme Calculator5 marks

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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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2
Sme Calculator5 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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3
Sme Calculator3 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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4
Sme Calculator6 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.

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