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,
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.