For this case we have the following variables, let:
x: The greater integer
y: The minor integer
We have to:
[tex]x + y = 2 (1)\\y-x = -14 (2)[/tex]
Thus, we have a system of two equations with two unknowns. To solve, we follow the steps below:
Step 1:
We add both equations:
[tex]x + y + y-x = 2-14\\2y = -12[/tex]
[tex]y = \frac {-12} {2}\\y = -6[/tex]
Thus, the smallest integer is [tex]y = -6[/tex]
Step 2:
We substitute "y" in any of the equations and clear x:
[tex]x + y = 2\\x + (- 6) = 2\\x-6 = 2\\x = 2 + 6\\x = 8[/tex]
Thus, the largest integer is [tex]x = 8[/tex]
So:
[tex]8 + (- 6) = 8-6 = 2\\-6-8 = -14[/tex]
Anwer:
Integer minor, [tex]y = -6[/tex]
Integer greater,[tex]x = 8[/tex]
