Mathematics
Form the pair of linear equations in the following problems, and find their solutions 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.
Linear Equations
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Answer
Let cost of one pencil be ₹ x and cost of one pen be ₹ y.
Given,
5 pencils and 7 pens together cost ₹ 50.
⇒ 5x + 7y = 50
⇒ 7y = 50 - 5x
⇒ y = ………(1)
Also,
7 pencils and 5 pens together cost ₹ 46.
⇒ 7x + 5y = 46
⇒ 5y = 46 - 7x
⇒ y = ………(2)
Table of values for equation (1),
| x | y |
|---|---|
| 3 | 5 |
| 10 | 0 |
Table of values for equation (2),
| x | y |
|---|---|
| 3 | 5 |
| 8 | -2 |
Steps of construction :
Plot the points (3, 5) and (10, 0) join them to form equation (1).
Plot the points (3, 5) and (8, -2) and join them to form equation (2).
The lines intersect at A(3, 5), which is the required solution.
Hence, linear equations pair are 5x + 7y = 50 and 7x + 5y = 46, where x is the cost of one pencil and y is the cost of one pen and cost of one pencil = ₹ 3 and cost of one pen = ₹ 5.
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