Question

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 

Answer 1

let cost of a pen be x and cost of pencil be y
acc. to first statement , 5y+7x=50_______(1)
rearranging equation, we get, x=(50-5y)/7
acc to second statement , 7y+5x=46---------(2)
substituting value of x in 2 ,
7y+5(50-5y)/7 = 46
 solving the equation we get , y=3 and x=5 
hence cost of one pen is 5 rs. and cost of one pencil is 3 rs.
HOPE IT HELPS :)

Answer 2

Let the cost of the pencil be x and pen be y
5 pencils &7 pens together cost Rs.50
i.e., 5x+7y = 50 ------ 1
7 pencils & 5 pens together costs Rs. 46
i.e., 7x+5y = 46 ------- 2

now,
multiply 1st equation with 7 and 2nd equation with 5 in order to cancel a pair of similar terms

eqn 1 × 7 i.e.,  7( 5x+7y = 50 )
                       35x+49y = 350 -------- 3
eqn 2 × 5 i.e.,   5( 7x+5y = 46 )
                        35x+25y = 230 -------- 4

now subtract eqn 4 from eqn 3
     
                        35x+49y = 350
                        35x+25y = 230
                       -       -         -
                    --------------------------------
                                24y = 120
                     --------------------------------
                        y = 120/24
                        y = 5
therefore, cost of the pen (y) = 5 Rs

substitute  y=5 in eqn 1. 5x+7y = 50
                5x+7(5) = 50
                5x = 50 - 35
                5x = 15
                 x = 3
therefore, cost of the pencil (x) = 3 Rs

Hence: Cost of each pen (y) is Rs. 5 and cost of each pencil (x) is Rs. 3