Question

5. Find the value of k for which the following equations are inconsistent: 2x + 3y = 4 ; (k + 2) * x + 6y = (3k + 2) ^ 2 (2)​

Answer 1

We know that the system of equations

a x+b y = c

¹ ¹ ¹

a x+b y = c

² ² ²

has infinitely many solutions, if

a b c

¹ = ¹ = ¹

a b c

² ² ²

Here, a = 2, b =3, c = 4,

¹ ¹ ¹

a = k+2,b = 6,c = 3k+2.

² ² ²

Therefore, the given system of equations will have infinitely many solutions, if

2 = 3 = 4

k + 2 6 3k+2

= 2 = 3 and 3 = 4

k + 2 6 6 3k+2

= 2 = 1 = 1 = 4

k + 2 2 2 3k+2

=k+2=4 and 3k+2=8

=k=2 and k=2

=k=2

Hence, the given system of equations will have infinitely many solutions, if k=2.

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