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First you have to understand what is meant by intersection. The question is asking what ordered pair appears in both equations.
Notice that it would be silly to assume that whatever point this may be, that the parameters t are equal in both equations (as pointed out above).
So begin by distinguishing the parameters.
So you should get:
(1, 0)x + (-1, 2)y = (1, 1)
Put this info in a matrix
(1 -1 1)
(0 2 1)
and reducing gives
(1 0 3/2)
(0 1 1/2)
which tells us they intersect when x = 3/2 and y =1/2.
plugging in to the original equations shows that this point is (3/2, 2)
