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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables5 Marks
Question

Form the pair of linear equations in the problem, and find its solution graphically:
5 pencils and 7 pens together cost ₹ 50 whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen.

✓

Answer

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 (2) by 5 we get
7(5x+7y)= 7 $\times$ 50
35x +49y = 350 .......(3)
and
5(7x +5y) = 5 $\times$ 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 = $\frac{120}{24}$
y= 5
Substitute y = 5 in equation 1 , we get
5x + 7 $\times$ 5 =50
5x + 35 = 50
5x = 50 - 35
5x = 15
x= $\frac{15}{5}$
x=3
Hence, Cost of One Pen = y =5

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