Question

3x + 4y – 17 = 0 and 2x + ky −34/3 = 0, have infinite number of solutions. Find ‘k’

Answer 1

Step-by-step explanation:

The equations are

$3x + 4y - k = 0 \\ 9x + 12y - 6 = 0$

Here,

$a_{1} = 3 \: \: \: b_{1} = 4 \: \: \: c_{1} = - k$

and

$a_{2} = 9 \: \: b_{2} = 12 \: \: \: \: c _{2} = - 6$

For the system to have infinite solution if

$\frac{ a_{1} }{ a_{2} } = \frac{ b_{1} }{b _{2} } = \frac{ c_{1} }{c _{2} } </p><p></p><p></p><p>$

$= \frac{3}{9} = \frac{4}{12} = \frac{ - k}{ - 6}$

$= 3k = 6$

$= k = 2$

✨hOpE iT HeLpS

✨ AkRiTi