C-12-Q017mediumsingle_mcq

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually independent when —

a $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$
b $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$
c $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$
d $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \ne \dfrac{c_1}{c_2}$

ব্যাখ্যা

A system has a unique solution (consistent and independent) precisely when the coefficient ratios differ, $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$ , so the two lines have different slopes and intersect at one point.

এই অধ্যায়ের আরও প্রশ্ন

C-12-Q018The system is consistent and mutually dependent when —
C-12-Q019The system is inconsistent and mutually independent when —
C-12-Q020If , the system is —
C-12-Q021If and , the system has —
C-12-Q022If and , the unique solution of the system is —
C-12-Q023To check consistency from coefficient ratios alone (without comparing constant terms), the equations must sati
C-12-Q024For a consistent independent system in two variables, the graphs of the two equations —
C-12-Q025The system is —
C-12-Q026The number of solutions of is —
C-12-Q027The system is —

Simple Simultaneous Equations in Two Variables — সব প্রশ্ন দেখুন (152টি) →

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually independent when —

\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}

\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}

\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}

\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \ne \dfrac{c_1}{c_2}

The system a1x+b1y=c1, a2x+b2y=c2a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2a1​x+b1​y=c1​,a2​x+b2​y=c2​ is consistent and mutually independent when —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

The system a1x+b1y=c1, a2x+b2y=c2a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2a1​x+b1​y=c1​,a2​x+b2​y=c2​ is consistent and mutually independent when —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually independent when —

The system $a_1 x + b_1 y = c_1,\; a_2 x + b_2 y = c_2$ is consistent and mutually independent when —