Your friend is thinking of two numbers. The sum of the two numbers is 34, and their difference is 12. Using the system of equations shown, what are the two numbers?

Question

{x+y=34x−y=12

(1 point)
Responses

23 and 11
23 and 11

17 and 12
17 and 12

21 and 9
21 and 9

19 and 15

Answer 1

To find the two numbers that your friend is thinking of, we can solve the system of equations given:

1. \( x + y = 34 \) (Equation 1)
2. \( x - y = 12 \) (Equation 2)

We can solve these equations step by step.

Step 1: Solve for \( x \) and \( y \)

First, we can add the two equations together:

\[ (x + y) + (x - y) = 34 + 12 \]

This simplifies to:

\[ 2x = 46 \]

Now, divide both sides by 2:

\[ x = 23 \]

Step 2: Find \( y \)

Now that we have \( x \), we can substitute \( x = 23 \) back into Equation 1 to find \( y \):

\[ 23 + y = 34 \]

Subtract 23 from both sides:

\[ y = 34 - 23 = 11 \]

Conclusion

The two numbers your friend is thinking of are 23 and 11.

So the correct response is:

23 and 11.