Simultaneous Equations (Cambridge O Level Maths)

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

 

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

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

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

is the total number of dots used to make all of the first  diagrams.

 

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

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

A counter is taken at random from the bag.

The probability that the counter is green is 

The counter is put back in the bag.

more red counters and  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 

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

Work out the value of 

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.