C-12-Q023mediumsingle_mcq

To check consistency from coefficient ratios alone (without comparing constant terms), the equations must satisfy —

a $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$ or both constants are zero
b $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$ always
c $a_1 = a_2$ and $b_1 = b_2$
d $c_1 = c_2 \ne 0$

ব্যাখ্যা

Consistency can be judged from coefficient ratios alone when $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$ (guaranteeing a unique solution), or when the system is homogeneous (both constants zero), which is always consistent regardless of the ratios.

এই অধ্যায়ের আরও প্রশ্ন

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 —
C-12-Q028The system is —
C-12-Q029The number of solutions of is —
C-12-Q030The system is —
C-12-Q031The number of solutions of is —
C-12-Q032The system is —
C-12-Q033The unique solution of is —

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

To check consistency from coefficient ratios alone (without comparing constant terms), the equations must satisfy —

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

or both constants are zero

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

always

a_1 = a_2

and

b_1 = b_2

c_1 = c_2 \ne 0