The price of 2 Note books and 3 pens is 69 Rupees . The price of 6 note book and 12 pens in 186 rupees . What is the price of a note book . What is the price of a pen
Answers
Answer:
(x,y) = (45,-7)
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Step-by-step explanation:
x is for notebooks
y is for pens
2x+3y = 69(xd)
6x+12y=186
3(2x+3y = 69)
6x+12y = 186
6x+9y=207
6x+12y = 186
-3y = 21
y = -7
2x+3(-7) = 69
2x-21 = 69
2x = 69+21
2x = 90
x=45
Let the price of one notebook be x and one pen be y.
Case I
The price of 2 Note books and 3 pens is 69 Rupees.
Therefore,
2x + 3y = 69 .....[1]
Case II
The price of 6 note book and 12 pens in 186 rupees
Therefore,
6x + 12y = 186
In this case, we can completely divide the whole equation by 6.
After dividing it by 6, We get,
x + 2y = 31 ....[2]
Now let's solve our equations [1] and [2]
2x + 3y = 69 ....[1]
x + 2y = 31 ....[2]
Multiplying [2] by 2 so that the coefficients of x becomes same in both eq.
2(x + 2y = 21) = 2x + 4y = 62
Now, Subtracting [1] from [2] will imply
2x + 3y = 69
-(2x + 4y = 61)
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-y = 7
y = -7
Since, earlier we Discussed that x + 2y = 31, Therefore, Substituting the value of y will imply,
x + 2y = 31
→ x +2(-7) = 31
→ x + (-14) = 31
→ x - 14 = 31
→ x = 31 + 14
→ x = 45
Hence, the cost of a notebook is ₹45 and a pen is ₹-7.
But since, it's impossible that cost of the pen will be negative, therefore the Question isn't valid for this.
Hence, the cost of a notebook is ₹45.