Question

2. Find the number of solutions of the pair of equations
x+2y-4=0 and 2x+4y-12-0.​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Equations are}$

$\mathsf{x+2y-4=0\;\;and\;\;2x+4y-12=0}$

$\underline{\textbf{To find:}}$

$\textsf{Number of solutions of the given equations}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Condition for no solution:}}$

$\textsf{Condtion for the equations}\;\mathsf{a_1x+b_1y+c_1=0\;and\;a_2x+b_2y+c_2=0\;have\;no\;solution\;is}$

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

$\mathsf{Here,}$

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

$\mathsf{\dfrac{b_1}{b_2}=\dfrac{2}{4}=\dfrac{1}{2}}$

$\mathsf{\dfrac{c_1}{c_2}=\dfrac{-4}{-12}=\dfrac{1}{3}}$

$\implies\mathsf{\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}{\neq}\dfrac{c_1}{c_2}}$

$\therefore\textsf{The given equations have no solution}$

$\underline{\textbf{Find more:}}$

Solve the following simultaneous equations for 2x-Y = -1 ; 3x-Y = 7​

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