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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.
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.
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