Question

Solve the following simultaneous equations

`1/(3x)-1/(4y)+1=0`;

`1/(5x)+1/(2y)=4/15`

Answer 1

`1/(3x)-1/(4y)+1=0` and `1/(5x)+1/(2y)=4/15`

`1/(3x)-1/(4y)=-1` and `1/(5x)+1/(2y)=4/15`

Let `1/x=a` and `1/y=b`

`a/3-b/4=-1` and `a/5+b/2=4/15`

`4a-3b=-12 and 2a+5b=40/15`

`4a-3b=-12 and 2a+5b=8/3`

`4a-3b=-12 and 6a+15b=8`

Solving thetwo equations, we get a=-2 and b=4/3

resubstituting `1/x=a and 1/y=b`

`=>x=-1/2 and y=3/4`