Solve this equation for x in terms of t using cramer's rule: (t)x+(2t+1)y=(t+1)

(t-1)x+(2t)y=t(t+1)

So our coefficient matrix is given by:


Taking the determinant of our coefficient matrix:


If we take the determinant of our coefficient matrix with x-column replaced by the answer column values:


Cramer's Rule tells us:


Applying Polynomial Long Division or Synthetic Division (with -1) should give you the result -2t^2+t if I did my calculations correctly.

This can be factored, giving us a nicer looking answer of 

This is a fairly long problem, easy to get confused along the way. Lemme know if anything didn't make sense.