Question

For what value of 'k' is the pair of linear equations X+2y=7 and 3X-KY=21 has infinitely many solutions?​

Answer 1

The value of k is "- 6".

Step-by-step explanation:

The pair of linear equations are

X + 2Y = 7 and 3X - KY = 21

This equations are of the form

$a_{1}$x + $b_{1}$y = $c_{1}$

$a_{2}$x + $b_{2}$y = $c_{2}$

Here, $a_{1}$ = 1, $b_{1}$ = 2, $c_{1}$ = 7 and

$a_{2}$ = 3, $b_{2}$ =  - k, $c_{2}$ = 21

The condition of infinite many solutions,

We must have:

$\dfrac{a_{1}}{a_{2} }$= $\dfrac{b_{1}}{b_{2} }$ = $\dfrac{c_{1}}{c_{2} }$

∴ $\dfrac{1}{3}$ = $\dfrac{2}{- k}$ = $\dfrac{7}{21}$

⇒  $\dfrac{1}{3}$ = $\dfrac{2}{- k}$ or $\dfrac{2}{- k}$ = $\dfrac{7}{21}$

⇒ k = - 6 or k = -6

Hence, the value of k is "- 6".