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Byju's Answer
Standard VIII
Mathematics
Linear Equations in One Variable
Solve the fol...
Question
Solve the following pair of equations:
x
a
−
y
b
=
0
,
a
x
+
b
y
=
a
2
+
b
2
A
x
=
b
−
a
and
y
=
b
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B
x
=
0
and
y
=
b
a
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C
x
=
b
a
and
y
=
b
a
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D
x
=
a
and
y
=
b
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Solution
The correct option is
B
x
=
a
and
y
=
b
The equation
x
a
−
y
b
=
0
can be rewritten as:
b
x
−
a
y
=
0...........
(
1
)
T
he other equation given i
s:
a
x
+
b
y
=
a
2
+
b
2
.
.
.
.
.
.
.
.
.
.
(
2
)
We pick either of the equations and write one variable in terms of the other.
Let us consider the equation
b
x
−
a
y
=
0
and write it as
x
=
a
y
b
Substitute the value of
x
in equation
a
x
+
b
y
=
a
2
+
b
2
. We get
a
(
a
y
b
)
+
b
y
=
a
2
+
b
2
⇒
a
2
y
b
+
b
y
=
a
2
+
b
2
⇒
a
2
y
+
b
2
y
b
=
a
2
+
b
2
⇒
(
a
2
+
b
2
)
y
=
b
(
a
2
+
b
2
)
⇒
y
=
b
Therefore,
y
=
b
Substituting this value of
y
in
the equation
x
=
a
y
b
, we get
x
=
a
b
b
=
a
Hence, the solution is
x
=
a
,
y
=
b
.
Suggest Corrections
1
Similar questions
Q.
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x
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x
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Question 9 (vi)
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