Question

One integer added to another integer gives a sum of 2. When the larger integer is subtracted from the smaller integer, the difference is -14. What could the two integers be? Explain.

Answer 1

For this case we have the following variables, let:

x: The greater integer

y: The minor integer

We have to:

$x + y = 2 (1)\\y-x = -14 (2)$

Thus, we have a system of two equations with two unknowns. To solve, we follow the steps below:

Step 1:

We add both equations:

$x + y + y-x = 2-14\\2y = -12$

$y = \frac {-12} {2}\\y = -6$

Thus, the smallest integer is $y = -6$

Step 2:

We substitute "y" in any of the equations and clear x:

$x + y = 2\\x + (- 6) = 2\\x-6 = 2\\x = 2 + 6\\x = 8$

Thus, the largest integer is $x = 8$

So:

$8 + (- 6) = 8-6 = 2\\-6-8 = -14$

Anwer:

Integer minor, $y = -6$

Integer greater,$x = 8$