Question

Please answer the question​

Answer 1

Answer:

The value of k is -9 and the value of m is 15

Explanation:

Given, the pair of linear equations

$2x+3y=5$            ............ (1)

$6x-ky=m$            ............ (2)

We know that if two simultaneous equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ have infinitely many solutions then

$\frac{a_1}{a_2} =\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore, for the equations (1) and (2) to have infinitely many solutions

$\frac{2}{6} =\frac{3}{-k}=\frac{5}{m}$

equating the first two

$\frac{2}{6} =\frac{3}{-k}$

$\implies k=-9$

Again equation the first and third

$\frac{2}{6} =\frac{5}{m}$

$\implies m=15$

Therefore k = -9 and m = 15