Question

Given the following system is consistent

x+y=1
tx+y=t
(1+t)x+2y=3

Find the exact value of t.

Answer 1

subtract the first from the second
xt - x = t-1
x(t-1) = t-1
x = 1, if t±1

in 1st:
1+y = 1
y = 0
in the last:
(1+t)(1) + 0 = 3
1+t = 3
t = 2

Answer 2

Subtracting the first equation from the second gives you:
t-1 = (t-1)x
Therefore x = 1.
The first equation tells you that y = 0.
The third equation requires that
1 + t = 3
t = 2