Question

. Find the value of k for which the following pair of
linear equations has a unique solution.
4x + 7y - 30 = 0
5x – 9ky + 20 = 0​

Answer 1

Question -

Find the value of k for which the following pair of

linear equations has a unique solution.

4x + 7y - 30 = 0

5x – 9ky + 20 = 0

Solution -

=>4x+7y-30=0

=>4x+7y+(-30)=0

Here,

$a_1 = 4$

$b_1 = 7$

$c_1 = - 30$

And,

=>5x-9ky+20=0

=> 5x+(-9k)y+20=0

Here,

$a_2 = 5$

$b_2 = - 9k$

$c_2 = 20$

Now,

For the given pair to have a unique solution-

$\frac{a_1}{a_2} \neq \: \frac{b_1}{b_2}$

Putting the values we will get -

$\frac{4}{5} \neq \frac{7}{ - 9k}$

By cross multiplying -

$- 9k \times 4 \neq \: 7 \times 5$

$- 36k \neq 35$

$k \neq \frac{35}{ - 36}$

$k \neq\frac{ - 35}{36}$

Therefore the value of k will be any real value except - 35/36.