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Byju's Answer
Standard XII
Mathematics
Consistency of Linear System of Equations
For what valu...
Question
For what values of m does the system of equations
3
x
+
m
y
=
m
and
2
x
−
5
y
=
20
have a solution satisfying the conditions
x
>
0
,
y
>
0
.
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Solution
The given equations are
3
x
+
m
y
−
m
=
0
and
2
x
−
5
y
−
20
=
0
Solving these equations, we get
x
=
25
m
2
m
+
15
,
y
=
2
m
−
60
2
m
+
15
For
x
>
0
25
m
2
m
+
15
>
0
⇒
m
<
−
15
2
or
m
>
0
.......(1)
For
y
>
0
2
(
m
−
30
)
2
m
+
15
>
0
⇒
m
<
−
15
2
or
m
>
30
.......(2)
Combining (1) and (2), we get the common values of
m
m
<
−
15
2
or
m
>
30
∴
m
∈
(
−
∞
,
−
15
2
)
∪
(
30
,
∞
)
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Similar questions
Q.
For what values of m does the system of equations
3
x
+
m
y
=
m
and
2
x
−
5
y
=
20
has a solution satisfying the condition x > 0, y > 0.
The ans is
m
∈
(
−
∞
−
15
2
)
∪
(
k
,
∞
)
Find the value of k?
Q.
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Q.
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