5 pencils and 7pens together cost $50, whereas 7 pencils and 5 pens together cost $46. Find the cost of one pencil and that of pen.

The correct answer is: 3, 5

let the cost of pencil be x and that of pen be y
so , 5 pencil + 7 pen = 50 , 5x + 7y = 50  eq1
and ,  7pencil + 5pen =  46 , 7x + 5y = 46  eq2
multiply eq1 with 7 and two with 5  and subtract eq2 from 1
step 1 :
doing , multiplication
35x + 49y = 350 eq1
and        35x + 25y = 230 eq2
step 2 :
perform subtraction
35x + 49y =    350      eq1
and      -(35x + 25y =   230 )     eq2
0   +  24y = 120   , solving for y we get y = 120/24 = 5
so , y= 5
step 3 :
put y = 5 in eq1
5x + 5*7 = 50 , solving we get x = 3
so , pencils cost 3 and pen costs 5