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Byju's Answer
Standard XII
Mathematics
Solving System of Linear Equations Using Inverse
For what valu...
Question
For what values of
a
does the following systems of equations have solutions? Find those solutions.
x
+
a
y
=
1
,
a
x
+
y
=
2
a
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Solution
Given equations,
x
+
a
y
=
1
→
(
1
)
a
x
+
y
=
2
a
→
(
2
)
(
1
)
×
a
−
(
2
)
⇒
(
a
2
−
1
)
y
=
−
a
y
=
a
1
−
a
2
For solution to be defined,
1
−
a
2
≠
0
a
≠
±
1
(
1
)
⇒
x
=
1
−
a
y
=
1
−
a
2
1
−
a
2
=
1
−
2
a
2
1
−
a
2
∀
a
=
I
R
−
{
−
1
,
1
}
, solution exists
Solution is
x
=
1
−
2
a
2
1
−
a
2
,
y
=
a
1
−
a
2
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0
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