Question

Check whether the pair of equations x+3y=6 and 2x-3y=12 is consistent.

Answer 1

$\textbf{Given:}$

$\textsf{Equations are}$

$\mathsf{x+3y=6\;\;and\;\;2x-3y=12}$

$\textbf{To find:}$

$\textsf{Check whether the pair of equations is consistent}$

$\textbf{Solution:}$

$\mathsf{Here,}$

$\mathsf{a_1=1,\;b_1=3,\;c_1=6}$

$\mathsf{a_2=2,\;b_2=-3,\;c_2=12}$

$\mathsf{\dfrac{a_1}{a_2}=\dfrac{1}{2}}$

$\mathsf{\dfrac{b_1}{b_2}=\dfrac{3}{-3}=-1}$

$\mathsf{\dfrac{c_1}{c_2}=\dfrac{6}{12}=\dfrac{1}{2}}$

$\implies\mathsf{\dfrac{a_1}{a_2}{\neq}\dfrac{b_1}{b_2}}$

$\therefore\textsf{The given pair of equations is consistent and}$

$\textsf{has unique solution}$

$\textbf{Find more:}$

Solve that the following pair of linear equations are consistent or inconsistent 5x-3y=11, 10x-6y=22​

https://brainly.in/question/22543281

on comparing the ratio a1/a2 , b1/b2 , c1/c2 Find out whether the pair 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 is consistent or inconsistent.​

https://brainly.in/question/31343425

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