Solve the following pair of linear equations: (ii) a/bx - b/ay = a + b ; ax - by= 2ab
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Step-by-step explanation:
Answer
Given equations can be written as
b
ax
−
a
by
=a+b⇒a
2
x−b
2
y−ab(a+b)=0 is in the form of a
1
x+b
1
y+c
1
ax−by=2ab⇒ax−by−2ab=0 is in the form of a
2
x+b
2
y+c
2
⇒a
1
=a
2
, b
1
=−b
2
, c
1
=−ab(a+b)
⇒a
2
=a , b
2
=−b , c
2
=−2ab
Using cross-multiplication method,
(b
1
)(c
2
)−(b
2
)(c
1
)
x
=
(c
1
)(a
2
)−(c
2
)(a
1
)
y
=
(a
1
)(b
2
)−(a
2
)(−b
1
)
1
(−b
2
)(−2ab)−(−b)(−ab(a+b))
x
=
(−ab(a+b))(a)−(−2ab)(a
2
)
y
=
(a
2
)(−b)−(a)(−b
2
)
1
2ab
3
−a
2
b
2
−ab
3
x
=
−a
3
b−a
2
b
2
+2a
3
b
y
=
−a
2
b+ab
2
1
ab
3
−a
2
b
2
x
=
a
3
b−a
2
b
2
y
=
ab
2
−a
2
b
1
ab
2
(b−a)
x
=
−a
2
b(b−a)
y
=
ab(b−a)
1
⇒
ab
2
(b−a)
x
=
ab(b−a)
1
or,x=b
⇒
−a
2
b(b−a)
y
=
ab(b−a)
1
or,y=−a
∴x=bandy=−a
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