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Question:

Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. (ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

Solution:

i) Consider number of boys=xand number of girls=y.According to the question,x+y=10or,y=10−x………(i)y=x+4………. (ii)x+y=10:-x1234y9876y=x+4:-x1234y5678Graphical solution : Girls=7,boys=3(ii) Consider price of a pencil isxand price of a pen isy.According to the question,5x+7y=50 (i)7x+5y=46.… (ii)7x+5y=46:-x1234y7.86.454.25x+7y=50:-x1234y6.45.754.2Graphical solution :Price of a pencil is Rs3Price of a pen is Rs5.