1. For every given number t, solve for   x, y the system

x+ty = 2, tx+y = -2

Solution. We solve the first equation for x:

x= 2 - ty.

We use this to eliminate x from the other equation:

t(2 - ty)+y = -2

or, in standard form, 

(1-t^2)y= -2-2t.

We solve this equation:

If t is not 1 or -1, then   y = 2/(t-1) and 

(substituting this to  x= 2 - ty)  

x = 2/(1-t).

If t = 1, then there are no solutions.

If t = -1, then y is arbitrary and x = 2+y.