Question

The pair of linear equations 2 x + 5 y = k , k x + 15 y =18 has infinitely many solutions if the value of k is:​

Answer 1

Step-by-step explanation:

The pair of linear equations

2x+5y=k

and kx+15y=18

Here,a

1

=2,b

1

=5,c

1

=−k

and a

2

=k,b

2

=15,c

2

=−18

The system of equation has infinitely many solutions if

a

2

a

1

=

b

2

b

1

=

c

2

c

1

⇒

k

2

=

15

5

=

−18

−k

⇒

k

2

=

3

1

=

18

k

Answer 2

Step-by-step explanation:

The condition for pair of linear equations in two variables where they has many solutions is a¹/a² = b¹/b² = c¹/c²

2x+5y-k=0 kx+15y-18=0

Here a¹ = 2 b¹=5 c¹= -k a² = k b²= 15 c²= -18

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