Question

1. three times a number added to another number is 18. two times the first number minus the other number is 2. what is the sum of the two numbers? type a response

Explanation:

Step1: Define variables

Let the first number be \( x \) and the second number be \( y \). From the problem, we have two equations:

1. \( 3x + y = 18 \) (Three times a number added to another number is 18)
2. \( 2x - y = 2 \) (Two times the first number minus the other number is 2)

Step2: Solve the system of equations

We can add the two equations together to eliminate \( y \):
\[

$$\begin{align*} (3x + y) + (2x - y) &= 18 + 2 \\ 3x + y + 2x - y &= 20 \\ 5x &= 20 \end{align*}$$

\]
Then, solve for \( x \):
\[
x = \frac{20}{5} = 4
\]

Step3: Find the value of \( y \)

Substitute \( x = 4 \) into the first equation \( 3x + y = 18 \):
\[
3(4) + y = 18 \\
12 + y = 18 \\
y = 18 - 12 \\
y = 6
\]

Step4: Calculate the sum of the two numbers

The sum of \( x \) and \( y \) is \( x + y = 4 + 6 = 10 \).

Answer:

10