Linear equation word problem

Question

A 13 foot board is cut into two pieces the length of the shorter piece is 1 foot more than half the length of the longer piece find the length in feet of the shorter piece? How many ft would that be?

Answer 1

Let x = length of short piece in feet

Let y = length of long piece in feet

The equations are x + y = 13 and x = .5y + 1

Solve simultaneously to get x = 5 and y = 8

The shorter piece is 5 feet and the longer piece is 8 feet.