Question

Two numbers, x and y, have a sum of 8 and a difference of –14. A. Write a system of equations that can be used to determine the values of x and y. B. Solve the system of equations. Show your work.

Answer 1

The system is:

x + y = 8

x - y = -14

And the solution is:

x = -3

y = 11

Explanation:

We have two numbers x and y, such that:

x + y = 8 (the sum is equal to 8)

x - y = -14 (the difference is equal to -14)

This is the system of equations we need to solve.

To solve the system, we first need to isolate one of the variables in one of the equations, I will isolate x in the first equation:

x = 8 - y

Now we can replace this in the other equation to get:

(8 - y) - y = -14

8 - 2*y = -14

8 + 14 = 2*y

22 = 2*y

22/2 = y

11 = y

Now we can replace this in the equation "x = 8 - y"

To get:

x = 8 - 11 = -3

Then the solution to the system is:

x = -3 and y = 11