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Quantitative Aptitude
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For what valu...
Question
For what value of ‘K’ will the following pair of linear equations have infinitely many solutions
Kx+3y=k-3; 12x+ky=k
[or kx+3y-k+3=0 ; 12x+ky-k=0]
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Solution
kx+3y=k-3
12x+ky=k
compare with
a
1
x
+
b
1
y
=
c
1
a
2
x
+
b
2
y
=
c
2
a
1
=
k
,
a
2
=
12
,
b
1
=
3
,
b
2
=
k
c
1
=
k
−
3
,
c
2
=
k
For infinite solutions,
a
1
a
2
=
b
1
b
2
=
c
1
c
2
∴
k
12
=
3
k
=
k
−
3
k
k
12
=
3
k
⇒
k
2
=
36
∴
k
=
6
.
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