Find the value of y if 2x-3y=9&value of x=6
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2X+3Y=[
2
4
3
0
] 3X+2Y=[
2
−1
−2
5
]
→ let Assume [
2
4
3
0
] = A
[
2
−1
−2
5
] = B
→2x+3y=A __ (i)
3x+2y=B __ (ii)
→ multiple equation (i) with 2 & equation (ii) with (3)
4x+6y=2A
9x+6y=3B
________________
−5x=2A−3B
∴x=
5
−1
[2A−3B]
∴x=
5
3B
−
5
2A
=
5
3
[
2
−1
−2
5
]−
5
2
[
2
4
3
0
]
=[
6/5
−3/5
−6/5
3
]−[
4/5
8/5
6/5
0
]
=[
6/5
−3/5
−4/5
−8/5
−4/5
3
−6/5
−0
]
∴x=[
1/5
−11/5
−12/5
3
]
→ value of x put in equation (i)
∴[
2/5
−22/5
−24/5
6
]+3y=[
2
4
3
0
]
∴3y=[
2−2/5
4+22/5
3+24/5
0−6
]=[
8/5
42/5
39/5
−6
]
∴y=[
8/15
42/15
39/15
−2
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