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Byju's Answer
Standard IX
Mathematics
Consistency and Inconsistency of Linear Equations in Two Variables
How many solu...
Question
How many solutions does the given system of equations has/have?
3
x
+
4
y
=
25
15
x
+
20
y
=
35
A
A unique solution.
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B
Infinitely many solutions
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C
No solution
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D
None of the above
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Solution
The correct option is
C
No solution
For a given pair of equations,
a
1
x
+
b
1
y
=
c
1
a
2
x
+
b
2
y
=
c
2
If
a
1
a
2
=
b
1
b
2
≠
c
1
c
2
,
then, the system of equations have no solution.
Here,
3
15
=
4
20
≠
25
35
So, the system of equations have no solution.
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Similar questions
Q.
If the given pair of equations has infinitely many solutions, then find the value of k?
3
x
+
4
y
=
k
15
x
+
20
y
=
35
Q.
Consider the simultaneous linear equations
3
x
+
4
y
=
1
And,
9
x
+
12
y
=
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.
How many solutions does this system of equations have?
Q.
−
6
x
+
8
y
=
2
,
3
x
−
4
y
=
−
3
Consider the system of equations above. How many
(
x
,
y
)
solutions does this system have?
Q.
For the following system of equation determine the value of k for which the given system of equation has infinitely many solutions.
5
x
+
2
y
=
k
10
x
+
4
y
=
3
Q.
Given equations are
3
x
−
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y
=
15
−
2
y
+
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y
=
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How many solution
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x
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