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 23 and 11 23 and 11 21 and 9 21 and 9 17 and 12 17 and 12 19 and 15

Answer 1

Let's solve the system of equations step by step.

We have two equations:

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

We can solve these equations using the elimination or substitution method. Here, we'll use the elimination method by adding the two equations together.

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 \( x \), we can substitute it back into Equation 1 to find \( y \):

\[ 23 + y = 34 \]

Subtract 23 from both sides:

\[ y = 34 - 23 \] \[ y = 11 \]

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

So the answer is 23 and 11.