Question

For what value of k, the pair of linear equations 4x + 6y -1 =0 and 2x + ky -7 = 0 represent parallel lines.

Answer 1

$\large\sf{\boxed{\underline{\red{Answer :-}}}}$

4x + 6y - 1 = 0 .... eq 1

2x + ky - 7 = 0 .... eq 2

Now,

Multiply eq 2 with 2 :-

$\implies$ 2x × 2 + ky × 2 - 7 × 2 = 0

$\implies$ 4x + 2ky - 14 = 0 .... eq 3

Solving eq 1 and eq 3 :-

4x + 6y - 1 = 0

4x + 2ky - 14 = 0

-ㅤ-ㅤㅤ+

_____________

6y - 2ky + 13 = 0

_____________

Now,

$\implies$ 6y - 2ky = - 13

$\implies$ y ( 6 - 2k ) = - 13

$\therefore$ y = $\dfrac{-13}{6\:-\:2k}$

*we can also find the value of x and k.

*By putting value of y in eq 1 we get value of x.

* Then we put value of x and y in eq 1 and get value of k.

$\large\underline{\overline{\mid\star\:{\sf{\green{Completed}}\:\star\mid}}}$