Question

find the value of P and Q for which the following system of equations has infinitely many solutions:
(2p- 1)x + 3y= 5 and 3x+ (q- 1)y=2​

Answer 1

$\textbf{Given:}$

$\textsf{The system of equations (2p-1)x+3y=5 and 3x+(q-1)y=2}$

$\textsf{has infinitely many solutions}$

$\textbf{To find:}$

$\textsf{The value of p and q}$

$\textbf{Solution:}$

$\underline{\textsf{Concept:}}$

$\mathsf{If\;the\;equations\;a_1x+b_1y=c_1\;and\;a_2x+b_2y=c_2\;have}$

$\mathsf{infinitley\;many\;solutions,\;then}$

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

$\textsf{Since the given system of equations have infinitely many solutions,}$

$\mathsf{\dfrac{2p-1}{3}=\dfrac{3}{q-1}=\dfrac{5}{2}}$

$\implies\mathsf{\dfrac{2p-1}{3}=\dfrac{5}{2}}$

$\implies\mathsf{2(2p-1)=15}$

$\implies\mathsf{4p-2=15}$

$\implies\mathsf{4p=15+2}$

$\implies\mathsf{4p=17}$

$\implies\boxed{\mathsf{p=\dfrac{17}{4}}}$

$\mathsf{and}$

$\implies\mathsf{\dfrac{3}{q-1}=\dfrac{5}{2}}$

$\implies\mathsf{6=(q-1)5}$

$\implies\mathsf{6=5q-5}$

$\implies\mathsf{5q=11}$

$\implies\boxed{\mathsf{q=\dfrac{11}{5}}}$

$\textbf{Find more:}$

Find the value (s) of a for which the system of equations below has infinitely many solutions.( a-3 )x +y = 0 and x+ (a-3)y =0

https://brainly.in/question/16026102