Pair of Linear Equations in Two Variables
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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.

Let cost of 1 pencil be Rs. ,v and cost of 1 pen be Rs. y

Case I. Cost of 5 pencils = 5x

Cost of 7 pens = 7y

<>According to question,

 

5x + 7y = 50

Case II. Cost of 7 pencils = 7x

Cost of 5 pens = 5y

According to question,

7x + 5y = 46

Thus, we have

Let cost of 1 pencil be Rs. ,v and cost of 1 pen be Rs. y Case I. Cos
Let cost of 1 pencil be Rs. ,v and cost of 1 pen be Rs. y Case I. Cos
Thus, we have following table :
Let cost of 1 pencil be Rs. ,v and cost of 1 pen be Rs. y Case I. Cos

Fig. 3.5.

When we plot the graph of the given equation, we find that both the lines intersect at the point (3, 5). So, x = 3,y = 5 is the required solution of the pair of linear equation.

Hence, the cost of 1 pencil be Rs. 3 cost of 1 pen be Rs. 5.

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