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Byju's Answer
Standard VIII
Mathematics
Solution of linear equation in 2 variables
If x = 2 - α...
Question
If
x
=
2
−
α
and
y
=
2
+
α
is a solution of the equation
3
x
−
2
y
+
6
=
0
find the value of '
α
'.
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Solution
Given equation,
3
x
−
2
y
+
6
=
0
x
=
2
−
α
,
y
=
2
+
α
is solution of given equation.
3
(
2
−
α
)
−
2
(
2
+
α
)
+
6
=
0
6
−
3
α
−
4
−
2
α
+
6
=
0
5
α
=
8
∴
α
=
8
5
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Similar questions
Q.
If
α
and
β
are solutions to the equation
2
y
2
y
+
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+
8
y
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3
=
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and
α
<
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, what is the value of
α
?
Q.
If
α
and
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are the roots of the quadratic equation
(
x
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)
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x
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3
)
(
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)
+
(
x
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)
(
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)
=
0
, then the value of
1
(
α
+
1
)
(
β
+
1
)
+
1
(
α
−
2
)
(
β
−
2
)
+
1
(
α
−
3
)
(
β
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3
)
is
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equations
λ
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
x
+
(
c
o
s
α
)
y
+
(
s
i
n
α
)
z
=
0
−
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
has a non-trivial solution. For
λ
=
1
, find all values of
α
which are possible
Q.
Let
λ
and
α
be real. Find the set of all values of
λ
for which the system of linear equation
λ
x
+
(
s
i
n
α
)
y
+
(
c
o
s
α
)
z
=
0
x
+
(
c
o
s
α
)
y
+
(
s
i
n
α
)
z
=
0
−
x
+
(
s
i
n
α
)
y
−
(
c
o
s
α
)
z
=
0
has a non-trivial solution. For
λ
=
1
, find all values of
α
Q.
If
α
=
tan
−
1
(
√
3
x
2
y
−
x
)
,
β
=
tan
−
1
(
2
x
−
y
√
3
y
)
, then find the value of:
α
−
β
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