Question

Solve the following systems of equations: $\dfrac{3}{x} - \dfrac{1}{y} = - 9$, \[\dfrac{2}{x} + \dfrac{3}{y} = 5\]

Answer 1

Hint: In these types of questions remember to multiply the equations by some constant value to make coefficients equal and simplify them to find the values of x and y.

Complete step-by-step answer:
Let $\dfrac{3}{x} - \dfrac{1}{y} = - 9$ be the equation 1 and \[\dfrac{2}{x} + \dfrac{3}{y} = 5\] be the equation 2
Multiplying equation 1 by 3 and equation 2 by 1
So we get \[3 \times (\dfrac{3}{x} - \dfrac{1}{y}) = 3 \times ( - 9)\], \[1 \times (\dfrac{2}{x} + \dfrac{3}{y}) = 1 \times 5\]
\[ \Rightarrow \]\[\dfrac{9}{x} - \dfrac{3}{y} = - 27\], \[\dfrac{2}{x} + \dfrac{3}{y} = 5\]
Now adding both the equations, we get,
\[\dfrac{2}{x} + \dfrac{9}{x} - \dfrac{3}{y} + \dfrac{3}{y} = - 27 + 5\]
\[ \Rightarrow \]\[\dfrac{{11}}{x} = - 22\]
\[ \Rightarrow \]\[x = \dfrac{1}{{ - 2}}\]
Now using the value of x to find the value of y
Putting the value of x in equation 2
\[ \Rightarrow \]\[\dfrac{{ - 2 \times 2}}{1} + \dfrac{3}{y} = 5\]
\[ \Rightarrow \]\[y = \dfrac{1}{3}\]
Therefore the value of x and y are $\dfrac{1}{{ - 2}},\dfrac{1}{3}$.

Note: In these types of questions first let $\dfrac{3}{x} - \dfrac{1}{y} = - 9$ be the equation 1 and \[\dfrac{2}{x} + \dfrac{3}{y} = 5\] be the equation 2 then multiply equation one by 3 and equation 2 by 1 then add both the equation and find the value of x then with the help of the value of x find the value of y.