1). Solve the following simultaneous equations.

Question

a) 3/x + 5/y = 4, 9/x + 4/y = 5
b) 3x +y - 1/2 = 2x -1/3 = 5x - 2y + 1/5

Answer 1

It'd be nice to have some of your work to look at, eh?

3/x + 5/y = 4
9/x + 4/y = 5
It gets messy to try and solve for x or y, so solve for 1/x instead.
1/y = (4-3/x)/5
thus,
9/x + 4/5 (4-3/x) = 5
45/x + 16 - 12/x = 25
33/x = 9
1/x = 9/33 = 3/11
so, x = 11/3
now plug in to find y.

The second problem looks like you'll have to solve two equations:
3x +y - 1/2 = 2x -1/3
5x - 2y + 1/5 = 2x -1/3

best to clear the fractions first, then just solve the usual ways.