The sum of the two numbers is 12. If one number is doubled and the other is left unchanged

The sum of the two numbers is 12. If one number is doubled and the other is left unchanged, then these numbers add up to 16. Find the original numbers.

Let the first number be x and the second y. By the condition of the problem, it is known that the sum of these two numbers is (x + y) or 12. If the first number is doubled, then it becomes equal to 2x, and the second number is left unchanged, then the sum of these numbers becomes (2x + y ) or 16. Let’s compose a system of equations and solve it.

{x + y = 12; 2x + y = 16.

From the first equation of the system, we express y through x.

y = 12 – x.

Let us substitute expression (12 – x) in the second equation instead of y.

2x + 12 – x = 16;

x = 16 – 12;

x = 4 – the first number;

y = 12 – x = 12 – 4 = 8.

Answer. (4; 8).