Answer:

Let pencil be x and let pen be y

5x+7y=50

7x+5y=46

multiply first equation by 7

35x+49y = 350

multiply second equation by 5

35x+25y=230

solving them we get 24Y=120 which gives y is 5 rupees

substituting in second equation we get x is 3 rupees

Step-by-step explanation:

5 pencils &7 pens together cost Rs.50 whereas 7 pencils & 5 pens together costs Rs. 46.find the cost of ONE pen & one pencil

Solution:

            let cost(in RS) of one pencil = x

            and cost (in RS) of one pen = y

Therefore , according to question

                     5x+7y = 50  ........ (1)

                    7x + 5y = 46  .........(2)

      Multiply equation 1 by 7 and equation by 5 we get

                        7(5x+7y)= 7*50

                        35x +49y = 350 .......(3)

                  and

                        5(7x +5y) = 5*46

                        35x +25y = 230 ....... (4)

Subtract equation 4 from equation 3 , we get

                           35x + 49y - 35x - 25y = 350 -230

                            49y -25y = 120

                            24y = 120

                                y = 120 /24

                                y= 5

Substitute y=5 in equation 1 , we get

                5x +  7*5 =50

                5x+35 =50

                5x = 50 - 35

                5x =15

                x= 15/5

                x=3

Hence Cost of One Pencil = x =3

          Cost  of One Pen =y =5

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