The price of 3 notebooks and 4 pens is 65 rupees and the price of 4 notebooks and 5 pens is 85 rupees. Find the price of a notebook and the price of a pen?
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Answer:
Let book, notebook, pen be x, y, z respectively.
2x+6y+3z=40
3x+4y+2z=35
5x+7y+4z=61
⎣
⎢
⎢
⎡
2
3
5
6
4
7
3
2
4
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
40
35
61
⎦
⎥
⎥
⎤
Apply R
1
→R
1
−R
2
⎣
⎢
⎢
⎡
−1
3
5
2
4
7
1
2
4
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
35
61
⎦
⎥
⎥
⎤
Now R
1
→(−R
1
)
⎣
⎢
⎢
⎡
1
3
5
−2
4
7
−1
2
4
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
−5
35
61
⎦
⎥
⎥
⎤
R
2
→R
2
−3R
1
& R
3
→R
3
−5R
1
⎣
⎢
⎢
⎡
1
0
0
−2
10
17
−1
5
9
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
−5
50
86
⎦
⎥
⎥
⎤
R
2
→
10
1
R
2
,
⎣
⎢
⎢
⎢
⎡
1
0
0
−2
1
17
−1
−
2
1
9
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
−5
5
86
⎦
⎥
⎥
⎤
R
3
−17R
2
,
⎣
⎢
⎢
⎢
⎢
⎡
1
0
0
−2
1
0
−1
2
1
2
1
⎦
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
−5
5
1
⎦
⎥
⎥
⎤
Now x−2y−z=5, y+
2
z
=5,
2
z
=1
⇒z=2,y=4,x=5.
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