What is the solution to the system of equations represented by the two equations? y=3/2x y=-1/2x 4

and as soon as possible

If you are referring to simultaneous equations (which I think you are), you make the two equations equal to each other.

Since, y is equal to 3/2x and y is also equal to -1/2x + 4,

 3/2x must be equal to -1/2x + 4

=> 3/2x=-1/2x + 4
=> 3/2x + 1/2x = 4
=> 4/2x= 4
=> 2x= 4
=> x=2

If x= 2, you can substitute this value in either of the two initial equations to find the value for y :-

     y=3/2x
=> y=3/2*( 2)
=> y=3

So your two values for x and y are 2,3