Question: Let \( x \) represent one number and let \( y \) represent the other number. The sum of two…

Let \( x \) represent one number and let \( y \) represent the other number. The sum of two numbers is \(-4\). If one number is 14. Use the given conditions to write a system of equations. Solve the system and find the numbers.

Write a system of equations:

A. \(\left\{ \begin{array}{l} x + y = -4 \\ x - y = 14 \end{array} \right.\)

B. \(\left\{ \begin{array}{l} x + y = 14 \\ x - y = -3 \end{array} \right.\)

C. \(\left\{ \begin{array}{l} x + y = -3 \\ x - y = 13 \end{array} \right.\)

D. \(\left\{ \begin{array}{l} x + y = 13 \\ x - y = -4 \end{array} \right.\)

Solve the system and find the numbers.

The numbers are \( x = \boxed{\phantom{0}} \) and \( y = \boxed{\phantom{0}} \).

Solution

Let’s solve the problem with the given conditions. The sum of two numbers is \(-4\). If one number is 14, the system of equations must satisfy the initial condition: \[ \begin{cases} x + y = -4 & \\ x - y = 14 & \end{cases} \] The correct choice is A. Now, solve the system: Add the two equations: \[ (x + y) + (x - y) = -4 + 14 \] Simplify: \[ 2x = 10 \] Divide by 2: \[ x = 5 \] Substitute \(x = 5\) into the first equation: \[ 5 + y = -4 \] Solve for \(y\): \[ y = -4 - 5 \] \[ y = -9 \] The numbers are \( x = 5 \) and \( y = -9 \).