College

Two times a number added to another number is 33. The first number minus two times the second is 4. Find the numbers.

There are 4 parts to this question:

1. Define your variables.

2. Write the system of equations.

3. Solve the system of equations.

4. Correctly identify and enter the solution.

Write the answer as an ordered pair (x, y) in the box below.

Answer :

Here's how you can solve the problem step by step:

1. Define your variables:

Let's use:
- [tex]\( x \)[/tex] to represent the first number.
- [tex]\( y \)[/tex] to represent the second number.

2. Write the system of equations:

Based on the problem statement, we can form two equations:
- The first equation comes from "Two times a number added to another number is 33." This translates to:
[tex]\[
2x + y = 33
\][/tex]
- The second equation comes from "The first number minus two times the second is 4." This translates to:
[tex]\[
x - 2y = 4
\][/tex]

3. Solve the system of equations:

We will solve these two equations simultaneously.

From the first equation:
[tex]\[
2x + y = 33 \tag{1}
\][/tex]

From the second equation:
[tex]\[
x - 2y = 4 \tag{2}
\][/tex]

Let's solve equation (2) for [tex]\( x \)[/tex]:
[tex]\[
x = 4 + 2y \tag{3}
\][/tex]

Substitute equation (3) into equation (1):
[tex]\[
2(4 + 2y) + y = 33
\][/tex]

Expanding:
[tex]\[
8 + 4y + y = 33
\][/tex]

Combine like terms:
[tex]\[
8 + 5y = 33
\][/tex]

Subtract 8 from both sides:
[tex]\[
5y = 25
\][/tex]

Divide by 5:
[tex]\[
y = 5
\][/tex]

Now, substitute [tex]\( y = 5 \)[/tex] back into equation (3):
[tex]\[
x = 4 + 2(5)
\][/tex]

Simplify:
[tex]\[
x = 4 + 10 = 14
\][/tex]

4. Correctly identify and enter the solution:

The solution, expressed as an ordered pair, is [tex]\((x, y) = (14, 5)\)[/tex].

This ordered pair means that the first number is 14 and the second number is 5.