Question

solve by substitution method :4/(p-3)+6/(q-4)=5 and 5/(p-3)-3/(q-4)=1



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Answer 1

$\textbf{Given:}$

$\frac{4}{p-3}+\frac{6}{q-4}=5$

$\frac{5}{p-3}-\frac{3}{q-4}=1$

$\textbf{To find:}$

$\text{p and q}$

$\frac{4}{p-3}+\frac{6}{q-4}=5$....(1)

$\frac{5}{p-3}-\frac{3}{q-4}=1$

$\text{This can be written as}$

$\frac{5}{p-3}-1=\frac{3}{q-4}$....(2)

$\text{Using (2) in (1), we get}$

$\frac{4}{p-3}+2(\frac{3}{q-4})=5$

$\implies\frac{4}{p-3}+2(\frac{5}{p-3}-1)=5$

$\implies\frac{4}{p-3}+\frac{10}{p-3}-2=5$

$\implies\frac{4}{p-3}+\frac{10}{p-3}=5+2$

$\implies\frac{14}{p-3}=7$

$\implies\frac{2}{p-3}=1$

$\implies\;p-3=2$

$\implies\;p=2+3$

$\implies\boxed{\bf\;p=5}$

$\text{Put p=5 in (2), we get}$

$\frac{5}{5-3}-1=\frac{3}{q-4}$

$\frac{5}{2}-1=\frac{3}{q-4}$

$\frac{3}{2}=\frac{3}{q-4}$

$\frac{1}{2}=\frac{1}{q-4}$

$\implies\;q-4=2$

$\implies\;q=2+4$

$\implies\boxed{\bf\,q=6}$

$\therefore\textbf{The solution is p=5 and q=6}$

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