Question

solve 41/x - 47/y=35 ,47/x - 41/y=60 fast Iwill give extra 50 points who will give me correct answer and him or her as Brainiest answer​

Answer 1

Answer:

The solution of the given linear equations is

$\displaystyle{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:\left(\:\dfrac{528}{1385}\:,\:\dfrac{528}{815}\:\right)\:}}}$

Step-by-step-explanation:

The given linear equations are

$\displaystyle{\sf\:\dfrac{41}{x}\:-\:\dfrac{47}{y}\:=\:35\:\quad\cdots\,(\:1\:)}$

$\displaystyle{\sf\:\dfrac{47}{x}\:-\:\dfrac{41}{y}\:=\:60\:\quad\cdots\,(\:2\:)}$

Now, by substituting $\displaystyle{\sf\:\dfrac{1}{x}\:=\:a\:\quad\&\quad\:\dfrac{1}{y}\:=\:b}$,

$\displaystyle{\sf\:\dfrac{41}{x}\:-\:\dfrac{47}{y}\:=\:35\:\quad\cdots\,(\:1\:)}$

$\displaystyle{\implies\sf\:41a\:-\:47b\:=\:35\:\quad\cdots\,(\:3\:)}$

$\displaystyle{\sf\:\dfrac{47}{x}\:-\:\dfrac{41}{y}\:=\:60\:\quad\cdots\,(\:2\:)}$

$\displaystyle{\implies\sf\:47a\:-\:41b\:=\:60\:\quad\cdots\,(\:4\:)}$

By adding equations ( 3 ) & ( 4 ), we get,

$\displaystyle{\sf\:41a\:-\:47b\:+\:(\:47a\:-\:41b\:)\:=\:35\:+\:60}$

$\displaystyle{\implies\sf\:41a\:-\:47b\:+\:47a\:-\:41b\:=\:95}$

$\displaystyle{\implies\sf\:88a\:-\:88b\:=\:95}$

$\displaystyle{\implies\sf\:a\:-\:b\:=\:\dfrac{95}{88}\:\qquad\cdots\,[\:Dividing\:by\:88\:]}$

$\displaystyle{\implies\boxed{\sf\:a\:=\:\dfrac{95}{88}\:+\:b}}$

By substituting this value in equation ( 4 ), we get,

$\displaystyle{\sf\:47a\:-\:41b\:=\:60\:\quad\cdots\,(\:4\:)}$

$\displaystyle{\implies\sf\:47\:\times\:\left(\:\dfrac{95}{88}\:+\:b\:\right)\:-\:41b\:=\:60}$

$\displaystyle{\implies\sf\:\dfrac{47\:\times\:95}{88}\:+\:47b\:-\:41b\:=\:60}$

$\displaystyle{\implies\sf\:\dfrac{4465}{88}\:+\:6b\:=\:60}$

$\displaystyle{\implies\sf\:6b\:=\:60\:-\:\dfrac{4465}{88}}$

$\displaystyle{\implies\sf\:6b\:=\:\dfrac{60\:\times\:88\:-\:4465}{88}}$

$\displaystyle{\implies\sf\:6b\:=\:\dfrac{5280\:-\:4465}{88}}$

$\displaystyle{\implies\sf\:6b\:=\:\dfrac{815}{88}}$

$\displaystyle{\implies\sf\:b\:=\:\dfrac{815}{88\:\times\:6}}$

$\displaystyle{\implies\boxed{\pink{\sf\:b\:=\:\dfrac{815}{528}}}}$

Now,

$\displaystyle{\sf\:a\:=\:\dfrac{95}{88}\:+\:b}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{95}{88}\:+\:\dfrac{815}{528}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{95\:\times\:6}{88\:\times\:6}\:+\:\dfrac{815}{528}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{570}{528}\:+\:\dfrac{815}{528}}$

$\displaystyle{\implies\sf\:a\:=\:\dfrac{570\:+\:815}{528}}$

$\displaystyle{\implies\boxed{\green{\sf\:a\:=\:\dfrac{1385}{528}}}}$

Now, by re-substituting values of a and b, we get,

$\displaystyle{\sf\:\dfrac{1}{x}\:=\:a}$

$\displaystyle{\implies\sf\:\dfrac{1}{x}\:=\:\dfrac{1385}{528}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:\dfrac{528}{1385}}}}}$

Now,

$\displaystyle{\sf\:\dfrac{1}{y}\:=\:b}$

$\displaystyle{\implies\sf\:\dfrac{1}{y}\:=\:\dfrac{815}{528}}$

$\displaystyle{\implies\underline{\boxed{\blue{\sf\:y\:=\:\dfrac{528}{815}}}}}$

∴ The solution of the given linear equations is

$\displaystyle{\boxed{\red{\sf\:(\:x\:,\:y\:)\:=\:\left(\:\dfrac{528}{1385}\:,\:\dfrac{528}{815}\:\right)\:}}}$