Question

If the pair of linear equations kx + 8y = 30 and x + k^2y = 29 has unique solution,
which of the following is true in respect of k ?
a) k = 2 b) k = -2 c) k is not equal to -2 d) k is not equal to plus or minus 2

Answer 1

Given :

The pairs of linear equations are

k x + 8 y = 30

x + k² y = 29

The equations has unique solutions

To Find :

The value of k

Solution :

The pairs of linear equations are

k x + 8 y = 30

x + k² y = 29

∵ For unique solution of two equations $a_1$ x + $b_1$ y + $c_1$ = 0 and $a_2$ x + $b_2$ y +$c_2$ = 0

 $\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$

So,   By compare with given equations

$\dfrac{k}{1}\neq \dfrac{8}{k^{2} }$

Or,    k³ ≠ 8

i.e     k ≠ $\pm$ 2

Hence, The value of k for which pair of linear equation is unique is k ≠ $\pm$ 2    Answer