Final answer:
To solve this problem, we can use a system of equations. Let's call the two numbers x and y. We know that the sum of the two numbers is 12, and their difference is 6. Using the method of substitution, we can find that the two numbers are 9 and 3.
Step-by-step explanation:
To solve this problem, we can use a system of equations. Let's call the two numbers x and y. We know that the sum of the two numbers is 12, so we can write the equation x + y = 12. We also know that the difference between the two numbers is 6, so we can write the equation x - y = 6.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
- From the first equation, we can solve for x in terms of y: x = 12 - y.
- Substitute this value of x into the second equation: (12 - y) - y = 6.
- Simplify and solve for y: 12 - 2y = 6. Subtract 12 from both sides: -2y = -6. Divide both sides by -2: y = 3.
- Now substitute this value of y back into the first equation to find x: x + 3 = 12. Subtract 3 from both sides: x = 9.
So the two numbers are 9 and 3.