Find the value of two numbers if their sum is 26 and their difference is 2. Write an equation or system of equations to solve the problem.(1 point) Responses 11 and 15 11 and 15 12 and 14 12 and 14 13 and 15 13 and 15 10 and 16

Answer 1

To solve for the two numbers, we can set up a system of equations based on the information given:

Let:

• \( x \) be the first number
• \( y \) be the second number

From the problem, we have the following equations:

1. \( x + y = 26 \) (the sum of the numbers)
2. \( x - y = 2 \) (the difference of the numbers)

Now we can solve this system of equations.

Step 1: Solve for \( x \) in terms of \( y \)

From equation (2): \[ x = y + 2 \]

Step 2: Substitute into equation (1)

Substituting \( x \) into equation (1): \[ (y + 2) + y = 26 \]

Step 3: Combine like terms

\[ 2y + 2 = 26 \]

Step 4: Solve for \( y \)

Subtract 2 from both sides: \[ 2y = 24 \] Now divide by 2: \[ y = 12 \]

Step 5: Substitute back to find \( x \)

Now, substituting \( y \) back into \( x = y + 2 \): \[ x = 12 + 2 = 14 \]

Conclusion

The two numbers are:

• \( x = 14 \)
• \( y = 12 \)

Thus, the two numbers are 12 and 14.