Question

ਸਮੀਕਰਣ ਪ੍ਰਣਾਲੀ ਦੇ ਜੋੜੇ x-4y-6=0 ਅਤੇ 3x-12y-18=0 ਦੇ ਕਿੰਨੇ ਹੱਲ ਹੋਣਗੇ?​

Answer 1

${\huge{\underbrace{\rm{QUESTION\;\checkmark}}}}$

How many solutions will there be to the pair of equation systems x-4y-6 = 0 and 3x-12y-18 = 0?

or

ਸਮੀਕਰਣ ਪ੍ਰਣਾਲੀ ਦੇ ਜੋੜੇ x-4y-6=0 ਅਤੇ 3x-12y-18=0 ਦੇ ਕਿੰਨੇ ਹੱਲ ਹੋਣਗੇ?

${\huge{\underbrace{\rm{ANSWER\;\checkmark}}}}$

$\longrightarrow \: x - 4y - 6 = 0$

In the above ↑ equation ,

$\star \: a_{1} = 1 \\ b_{1} = - 4 \\ c_{1} = - 6$

And ,

$\longrightarrow \: 3x - 12y - 18 = 0$

In the above ↑ equation ,

$\star \: a_{2} = 3 \\ b_{2} = - 12 \\ c_{2} = - 18$

Now ,

$\mapsto \: \frac{ a_{1} }{ a_{2} } = \frac{1}{3} \\ \\ \mapsto \: \frac{ b_{1} }{ b_{2} } = \frac{ - 4}{ - 12} = \frac{1}{3} \\ \\ \mapsto \: \frac{ c_{1}}{ c_{2} } = \frac{ - 6}{ - 18} = \frac{1}{3}$

Clearly here ,

$\leadsto \: \frac{ a_{1} }{ a_{2} } = \frac{ b_{1} }{ b_{2} } = \frac{ c_{1}}{ c_{2} } \\ \\ \therefore \: \rm it \: has \: infinte \: solutions$

$\boxed{ \star \: infinte \: solutions}$