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NIMCET 2009 Question Paper with solutions
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© examsnet.com
Question : 5
Total: 120
If
a
+
b
+
c
neq
0
, then the system of equations
(
b
+
c
)
(
y
+
z
)
−
a
x
=
b
−
c
(
c
+
a
)
(
z
+
x
)
−
b
y
=
c
−
a
(
a
+
b
)
(
x
+
y
)
−
c
z
=
a
−
b
has
a unique solution
no solution
infinite number of solutions
finitely many solutions
Validate
Solution:
By adding the three. given equations, we get
(
a
+
b
+
c
)
(
x
+
y
+
z
)
=
0
⇒
x
+
y
+
z
=
0
Here,
x
=
c
−
b
a
+
b
+
c
,
y
=
a
−
c
a
+
b
+
c
and
z
=
b
−
a
a
+
b
+
c
,
a
+
b
+
c
≠
0
So, there are infinitely many solutions.
© examsnet.com
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