Question:The cost of 5 oranges and 4 lemons  is 23 new pence.The  cost of 3 oranges and 5 is 19 new pence.find the cost of an orange.. 

Answer The cost of 5 oranges and 4 lemons is (5x + 4y) new pence.
The cost of 3 oranges and 5 lemons is (3x + 5y) new pence.

                                          `:.  5x + 4y =23  . . . . . . . . . . . . . . . . . . .(1) 
                                                  3x + 5y =19  . . . . . . . . . . . . . . . . . . .(2)`

Multiply (1) by 3 :        15x + 12y = 69
Multiply (2)  by 5 :       15x + 25y = 95

Subtract :                     - 13y = - 26  
                                  `:.` y = 2 

substitute in (1)            5x + 8 = 23

                                `:.`5x =23 - 8

                                           = 15

                                  `:.` x = 3.

The cost of an orange is 3 new pence ; the cost of a lemon is  2 new pence .. 

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