Question

cud u help me with this question ​

Answer 1

》First question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Solution\:is\:Inconsistent}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies x + 2y = 4 \\ \\ \tt: \implies 3x + 6x = 12 \\ \\ \red{\underline \bold{To\:Find: }} \\ \tt: \implies Consistent \: or \: Inconsistent = ?$

• According to given question

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{1}{3} \\ \\ \tt: \implies \frac{ b_{1} }{ b_{2}} = \frac{2}{6} = \frac{1}{3} \\ \\ \tt: \implies \frac{ c_{1} }{ c_{2}} = \frac{4}{12} = \frac{1}{3} \\ \\ \text{From \: these \: eqn} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{ b_{1} }{ b_{2}} = \frac{ c_{1} }{ c_{2}} \\ \\ \green{\tt{ \therefore Solution \: is \: \: Inconsistent}}$

》Second question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Solution\:is\:consistent}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies x + 3y = 6 \\ \\ \tt: \implies 2x - 3x = 12 \\ \\ \red{\underline \bold{To\:Find: }} \\ \tt: \implies Consistent \: or \: Inconsistent = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{1}{2} \\ \\ \tt: \implies \frac{ b_{1} }{ b_{2}} = \frac{ - 3}{3} = - 1 \\ \\ \tt: \implies \frac{ c_{1} }{ c_{2}} = \frac{6}{12} = \frac{1}{2} \\ \\ \text{From \: these \: eqn} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{ c_{1} }{ c_{2}} \: \cancel = \: \frac{ b_{1} }{ b_{2}} \\ \\ \green{\tt{ \therefore Solution \: is \: \: Consistent}}$

》Third question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Solution\:is\:Inconsistent}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies 2x - 5y = 4 \\ \\ \tt: \implies 6x - 15y = 12 \\ \\ \red{\underline \bold{To\:Find: }} \\ \tt: \implies consistent \: or \: Inconsistent = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{2}{6} = \frac{1}{3} \\ \\ \tt: \implies \frac{ b_{1} }{ b_{2}} = \frac{ - 5}{ - 15} = \frac{1}{3} \\ \\ \tt: \implies \frac{ c_{1} }{ c_{2}} = \frac{4}{12} = \frac{1}{3} \\ \\ \text{From \: these \: eqn} \\ \tt: \implies \frac{ a_{1} }{ a_{2}} = \frac{ c_{1} }{ c_{2}} = \frac{ b_{1} }{ b_{2}} \\ \\ \green{\tt{ \therefore Solution \: is \: \: Inconsistent}}$