Designate the two numbers x and y.

x = 5 + 2y (one number is 5 more than twice another)

x + y - 10 = 22 (their sum decreased by 10 is 22)

Substitute for x in the second equation

(5 + 2y) + y - 10 = 22

3y - 5 = 22 (collect terms)

3y = 27 (add 5 to both sides)

y = 9 (divide both sides by 3)

x = 5 + 2(9) = 5 + 18 = 23 (compute x from first equation)

The two numbers are 9 and 23.

x = 5 + 2y (one number is 5 more than twice another)

x + y - 10 = 22 (their sum decreased by 10 is 22)

Substitute for x in the second equation

(5 + 2y) + y - 10 = 22

3y - 5 = 22 (collect terms)

3y = 27 (add 5 to both sides)

y = 9 (divide both sides by 3)

x = 5 + 2(9) = 5 + 18 = 23 (compute x from first equation)

The two numbers are 9 and 23.