Maths help: Solve the following simultaneous equation.

Question

5/x + 7/y = 31, 7y + 5x = 29xy.?

Answer 1

The simultaneous equations are

5/x + 7/y = 31     .....................................(1)

5x + 7y = 29xy   ......................................(2)

Re-write the equation (1)

5y + 7x = 31xy    .....................................(3)

Re-write the equation (2)

5x + 7y = 29xy

5x + 7y - 29xy

5x + y(7 - 29x) = 0

y = -5x/(7 - 29x)    .....................................(4)

Now substitute the value of y in equation (3)

Now if x = 0 then

y = -5x/(7 - 29x)       (From Equation (4))

y = 0

Similarly if x = 1/2

y = -5x/(7 - 29x)       (From Equation (4))

y = -5(1/2)/(7 - 29(1/2))

y = 1/3

Therefore the points are (0,0) and (1/2, 1/3).