Question

Find the value of k for which pair of linear equations 2x + ky = 4 and 6x + 9y = 12 has infinitely many solutions ​

Answer 1

⬛Given Question⬛

Find the value of k for which pair of linear equations 2x + ky = 4 and 6x + 9y = 12 has infinitely many solutions .

⬛Solution⬛

An equation is a combination of constants and variables and is in the form ax+by+c.

The formula for infinitely many solutions is ;

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

Given both the equations are :

2x+ky-4=0

6x+9y-12=0

Here, a1 =2, b1=k, c1=(-4) and a2=6,b2=9,c2=(- 12).

Therefore,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

$\frac{2}{6} = \frac{k}{9} = \frac{ - 4}{ - 12}$

$\frac{1}{3} = \frac{k}{9}$

$k = \frac{9}{3} = 3$

Thus, value of k is 3.