Find out the value of c for which the pair of equations cx – y = 2 and 6x – 2y =4 will have infinitely many solutions.
(A) 3
(B) – 3
(C) –12
(D) 4
Answers
Answer:
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Answer:
For no value of c the pair of equations will have infinitely many solutions.
Step-by-step explanation:
Given : The pair of equation cx-y=2cx−y=2 and 6x-2y=36x−2y=3 will have infinitely many solution.
To find : The value of 'c'?
Solution :
Condition for infinitely many solutions is
\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}
a
2
a
1
=
b
2
b
1
=
c
2
c
1
Given lines are cx-y=2cx−y=2 and 6x-2y=36x−2y=3
So, a_1=c,b_1=-1,c_1=-2,a_2=6,b_2=-2,c_2=-3a
1
=c,b
1
=−1,c
1
=−2,a
2
=6,b
2
=−2,c
2
=−3
Substitute in the condition,
\frac{c}{6}=\frac{-1}{-2}=\frac{-2}{-3}
6
c
=
−2
−1
=
−3
−2
\frac{c}{6}=\frac{1}{2}=\frac{2}{3}
6
c
=
2
1
=
3
2
Take first two,
\frac{c}{6}=\frac{1}{2}
6
c
=
2
1
Solve,
c=3c=3
Take first and last,
\frac{c}{6}=\frac{2}{3}
6
c
=
3
2
Solve,
c=4c=4
Since, c has different values.
Hence, For no value of c the pair of equations will have infinitely many solutions.
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