Write down the condition for which the following pair of linear equations for unique solution and find the value of k.
3x +5y =7
6x+7y=3
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Answer:
ﾑɳรᏇɛƦ
The straight lines : 2x+ky=1
3x−5y=7
Comparing 2x+ky=1
with a¹
x+b¹
y+c ¹ =0
a¹ =2,b¹ =k,c¹
=−1
Comparing 3x−5y=7
with a² x+b² y+c² =0
a²=3,b² =−5,c²
=−7
∴ For a unique solution ,
a²
a¹
=
b
2
b
1
⇒
3
2
=
−5
k
∴k
=
3
−10
For infinite solutions ,
a
2
a
1
=
b
2
b
1
=
c
2
c
1
⇒ 32
=
−5
k
=
7
1
thereisnosuchvalueofkwhichwillsatisfytheequation
For no solutions :
a
2
a
1
=
b
2
b
1
=
c
2
c
1
⇒
3
2
=
−5
k
∴k=−
3
10
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