Question

the pair of equations 5x-15y=8 and 3x-9y=24/5 has(a) one solution (b) two solution (c) Infinitely many solution (d) None of these

Answer 1

$\textbf{Given:}$

$\textsf{Equations are}$

$\mathsf{5x-15y=8}$

$\mathsf{3x-9y=\dfrac{24}{5}}$

$\textbf{To find:}$

$\textsf{The type of solution of given equations}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{8cm} \\\mathsf{Equations\;\;a_1x+b_1+c_1=0\;\&\;a_2x+b_2+c_2=0\;have}\\\\\mathsf{infinitely\;many\;solutions\;if\;\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{a_1}{a_2}=\dfrac{5}{3}}$

$\mathsf{\dfrac{b_1}{b_2}=\dfrac{-15}{-9}=\dfrac{5}{3}}$

$\mathsf{\dfrac{c_1}{c_2}=\dfrac{-8}{-24/5}=\dfrac{40}{24}=\dfrac{5}{3}}$

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

$\therefore\textsf{The equations have infinitely many solutions}$

$\textbf{Find more:}}$

Answer 2

Step-by-step explanation:

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