let

x = the length of the first piece

y = the length of the second piece

One piece of pipe 21 meters long is to be cut into two pieces:

x + y = 21

with the lengths of the pieces being in a 2:5 ratio:

x : y = 2 : 5 cross-multiply

5x = 2y

by solving the system of equations:

x + y = 21

5x = 2y

........

click here to see all the system of equations solution steps

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x = 6 m

y = 15 m

The lengths of the pieces are 6 meters and 15 meters.