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? {x+y=34x−y=12 (1 point) Responses 17 and 12 17 and 12 21 and 9 21 and 9 23 and 11 23 and 11 19 and 15

Answer 1

To solve for the two numbers, we can use the system of equations given:

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

We can solve this system by using the elimination or substitution method. Here, we will use the elimination method.

Start by adding Equation 1 and Equation 2:

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

This simplifies to:

\[ 2x = 46 \]

Now, divide both sides by 2:

\[ x = 23 \]

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

\[ 23 + y = 34 \]

Subtract 23 from both sides:

\[ y = 34 - 23 = 11 \]

Thus, the two numbers are \( x = 23 \) and \( y = 11 \).

So the answer is 23 and 11.