Write the algebraic representation of the situation, "the sum of two numbers is 137 and their difference is 43."

Options

A. x- y = 137,x + y = 43
B. x + y = 137,x- y = 43
C. 2x + y = 137, x- y = 43
D. x + 2y = 137,x-2y = 43

Answer

To represent the situation algebraically, we can follow these steps:

1. **Define the Variables**:
Let the first number be represented as \( x \) and the second number as \( y \).

2. **Write the Equation for the Sum**:
According to the problem, the sum of the two numbers is 137. This can be expressed as:
\[ x + y = 137 \]

3. **Write the Equation for the Difference**:
The problem also states that the difference between the two numbers is 43. This can be expressed as:
\[ x - y = 43 \]

4. **Combine the Equations**:
Now we have two equations:
\[ x + y = 137 \quad \text{(1)} \]
\[ x - y = 43 \quad \text{(2)} \]

Thus, the algebraic representation of the situation is:
\[ \begin{align*} x + y &= 137 \\ x - y &= 43 \end{align*} \]