Ex 3.1, 1 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Ex 3.1, 1
Form the pair of linear equations in the following problems & find their solutions graphically
(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
Let the Cost of one Pencil be Rs x
& Cost of one Pen be Rs y
Given that
5 pencils and 7 pens together cost Rs 50
5 × (Cost of pencil) + 7 × (Cost of pens) = 50
5x + 7y = 50
Also,
7 pencils and 5 pens together cost Rs. 46
7 × (Cost of pencil) + 5 × (Cost of pen) = 46
7x + 5y = 46
Now, plotting equations
5x + 7y = 50 ...(1)
7x + 5y = 46 …(2)
For Equation (1)
5x + 7y = 50
Let y = 5
5x + 7(5) = 50
5x + 35 = 50
5x + 35 = 50 − 35
5x = 15
x = 15/5
x = 3
So, x = 3, y = 5 is a solution
i.e. (3, 5) is a solution
Let x = 0
5(0) + 7y = 50
7y = 50
y = 50/7
y = 7.14
So, x = 0, y = 7.14 is a solution
i.e. (0, 7.14) is a solution
For Equation (2)
7x + 5y = 46
Let y = 0
7x + 5(0) = 46
7x = 46
x = 46/7
x = 6.57
So, x = 6.57, y = 0 is a solution
i.e. (6.57, 0) is a solution
Let x = 3
7(3) + 5y = 46
21 + 5y = 46
5y = 46 − 21
5y = 25
y = 25/5
y = 5
So, x = 3, y = 5 is a solution
i.e. (3, 5) is a solution
We will plot both equations on the graph
Therefore,
Solution of the equations is (3, 5)
Thus,
Cost of 1 Pencil = x = Rs 3
Cost of 1 Pen = y = Rs 5

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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