Questions: The sum of two numbers is -3. The difference of the two numbers is -11. What are the two numbers? The first number = The second number =

Solution Steps

To solve the problem of finding two numbers given their sum and difference, we can set up a system of linear equations. Let the two numbers be \( x \) and \( y \). We have the following equations based on the problem statement:

1. \( x + y = -3 \)
2. \( x - y = -11 \)

We can solve this system of equations using substitution or elimination methods. Here, we'll use the elimination method to find the values of \( x \) and \( y \).

We are given two conditions:

1. The sum of two numbers is \(-3\): \[ x + y = -3 \]
2. The difference of the two numbers is \(-11\): \[ x - y = -11 \]

To solve the system, we can use the elimination method. Adding the two equations: \[ (x + y) + (x - y) = -3 + (-11) \] \[ 2x = -14 \] \[ x = -7 \]

Next, substitute \( x = -7 \) back into the first equation: \[ -7 + y = -3 \] \[ y = -3 + 7 \] \[ y = 4 \]

Final Answer