Question

what will be the type of equation if a1/a2≠b1/b2≠c1/c2 is the compared ratio of any equation​

Answer 1

$\large\underline{\boxed{\red{\tt Given :- }}}$

• $\sf The \:ratio \:of \:coefficients \:of\:\\\sf equation\: is\: , \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

$\large\underline{\boxed{\red{\tt To\:Find:- }}}$

• $\sf The\:type\:of\:equ^n .$

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

$\sf The \:standard \:form \:of \:two\: linear\: equations \\\sf \:in\: two \:variables\: are ,$

• $\sf a_1x+b_1y+c_1=0$
• $\sf a_2x+b_2y+c_2 = 0$

$\underline{\blue{\sf For \:given\: condition \:of\: co-efficients:-}}$

$\boxed{\pink{\bf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2} }}$

$\sf The\: given\:pair\:of\:lines \: will\:have\: no\: solution.\\\sf That\:is\:the\:lines\:are\:parallel.$

$\underline{\underline {\green{\bf A\: example \:of\:above\: condition:- }}}$

$\tt Let \:us \:consider\: two \;lines ,$

• $\sf 2x + y + 5 = 0$
• $\sf 4x + 2y + 7 = 0$

$\underline{\sf If \:we \:find\: Ratio\:of\: coefficients ,}$

$\tt:\implies \bigg\lgroup\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2} \bigg\rgroup= \cancel{\dfrac{ 2}{4}}=\cancel{\dfrac{1}{2}}\neq \dfrac{5}{7}$

$\underline{\boxed{\purple{\tt\longmapsto\bigg\lgroup\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2} \bigg\rgroup= \dfrac{1}{2}=\dfrac{1}{2}\neq \dfrac{5}{7}}}}$

If we plot the graph of both the equations , then we will see that the given lines won't intersect each other . And will be parallel .

$\sf \lgroup Graph \:in\: attachment :- \rgroup$