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Byju's Answer
Standard X
Mathematics
Equations Reducible to a Pair of Linear Equations in Two Variables
Solve the fol...
Question
Solve the following system of equations,
1
2
x
−
1
y
=
−
1
and
1
x
+
1
2
y
=
8
, where
x
≠
0
,
y
≠
0
.
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Solution
Taking
1
x
=
u
and
1
y
=
v
, the given equations become
u
2
−
v
=
−
1
⇒
u
−
2
v
=
−
2
.(i)
and,
u
+
v
2
=
8
⇒
2
u
+
v
=
16
.(ii)
Let us eliminate u from equations (i) and (ii). Multiplying equation (i) by
2
, we get
2
u
−
4
v
=
−
4
..(iii)
2
u
+
v
=
16
(iv)
Subtracting (iv) from (iii), we get
−
5
v
=
−
20
⇒
v
=
4
Putting
v
=
4
in equation (i), we get
u
−
8
=
−
2
⇒
u
=
6
Hence,
x
=
1
u
=
1
6
and
y
=
1
v
=
1
4
So, the solution of the given system of equation is
x
=
1
6
,
y
=
1
4
.
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Similar questions
Q.
Solve the following systems of equations
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Q.
Question 9 (iv)
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