Question

Write two equations:
#1 The difference between the two numbers is 3.
#2 The sum of the two numbers is 13.

What are the two numbers?
Let x = _____________
Let y =______________

Answer 1

Let's write the two equations based on the information provided:

1. The difference between the two numbers is 3:
\( x - y = 3 \)

2. The sum of the two numbers is 13:
\( x + y = 13 \)

Now we can solve the equations.

From the first equation, we can rearrange it to express \( x \) in terms of \( y \):
\[ x = y + 3 \]

Now we can substitute this expression for \( x \) into the second equation:
\[ (y + 3) + y = 13 \]

Combining like terms:
\[ 2y + 3 = 13 \]

Subtracting 3 from both sides:
\[ 2y = 10 \]

Dividing by 2:
\[ y = 5 \]

Now we can find \( x \) using the expression we found earlier:
\[ x = y + 3 \]
\[ x = 5 + 3 = 8 \]

So the two numbers are:
Let \( x = 8 \)
Let \( y = 5 \)