Form the pair of linear equations in the following problems, and … - Vidyadip

Question

Form the pair of linear equations in the following problems, and find their solution graphically:
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 a pen.

✓

Answer

Let the number of pencils and pens be x and y respectively.
According to questions.
5x + 7y = 50 .......(i)
7x + 5y = 46 ........(ii)
From (i), $\text{y}=\frac{50-5\text{x}}{7}\ ......(\text{iii})$
Putting x = 3 in (iii), we get y = 5
Putting x = -4 in (iii), we get y = 10

x	3	-4
y	5	10

From (ii), $\text{y}=\frac{46-7\text{x}}{5}\ ......(\text{iv})$
Putting x = 3 in (iv), we get y = 5
Putting x = -2 in (iv), we get y = 12

x	3	-2
y	5	12

Thus, from graph cost of pencil = Rs. 3 and cost of pen= Rs. 5.

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