Question

Determine the values of m and n so that following pair of liner equations have infinite number of solutions $(2m-1)x+3y=5;3x+(n-1)y=2$.

Answer 1

Given Lines will have infinite solutions if these lines are concurrent or they have the same Equation

$(2m-1)x+3y=5\Rightarrow \frac{2m-1}{5}x+\frac{3}{5}y=13x+(n-1)y=2\Rightarrow \frac{3}{2}x+\frac{n-1}{2}y=1$

Now, Equating the coefficient of x and y , we get

$\frac{2m-1}{5}=\frac{3}{2}\Rightarrow m=\frac{17}{4}\frac{n-1}{2}=\frac{3}{5}\Rightarrow n=\frac{11}{5}$