The sum of two numbers is 2 and their difference is 26.?

Question

a. Write a system of two equations with two variables for the problem.

b. What are the two numbers?

Answer 1

Let the numbers be x and y and let x > y

x + y = 2 ..... (1)
x - y = 26 ..... (2)

Adding both equations,

x + y + x - y = 26 + 2
2x = 28
x = 14

Put x = 14 in (2),

14 - y = 26
-y = 12
y = -12

The numbers are 14 and -12

Answer 2

x+y=2 x-y=26

y+26+y=2 x=26+-12
y= -12 x= 14