Question

solve the following system of equations
4x + 5y = 20xy
5x + 4y = 18xy (x not = 0 , y not = 0)​

Answer 1

Given:

The given system of equations are

4x + 5y = 20xy

5x + 4y = 18xy (x not = 0 , y not = 0)​

To find:

We have to solve the given equations i.e., find the values of x and y

Solution:

Consider  $4x+5y=20xy$ as equation _ _(1)

                 $5x+4y=18xy$ as equation _ _(2)

Now perform the operation 5(equation(1)) - 4(equation(2))

             $5(4x+5y=20xy)$

             -  $[4(5x+4y=18xy)]$

          =     $25y-16y = 100xy-72xy$

          =     $9y=28xy$

                 $28x=9$

                     $x=\frac{9}{28}$

Substitute   $x=\frac{9}{28}$ in equation (1)

⇒$4(\frac{9}{28})+5y = 20(\frac{9}{28})y$

⇒$y(5-\frac{45}{7})=\frac{9}{7}$

⇒$y(\frac{35-45}{7})=\frac{9}{7}$

⇒$y(\frac{-10}{7}) =\frac{9}{7}$

⇒$-10y=9$

⇒$y=\frac{-9}{10}$

∴$x=\frac{9}{28}$ and $y=\frac{-9}{10}$