A twelve foot piece of string is cut into two pieces so that the longer piece is three feet longer than twice the shorter piece. find the lengths of both pieces

Longer piece = two times the shorter piece plus 3 feet

L = 2S + 3

Two variables means you need 2 equations. Try adding the two pieces together like so:

L + S = 12 feet

Solve for L:

L = 12 - S

Then Substitute L in the other equation:

(12 - S) = 2S + 3

Solve for S, then put S back into the L = 12 - S equation and solve for L. : - )