The sum of three times the larger of the two integers and twiec the smaller integer is - 19. the difference between the two integer is 7. What are the integers?

The sum (addition) of 3 * the larger (y) + 2 * the smaller (x) = - 19

The difference (subtraction) between x & y

(y-x) = 7

3y + 2x = - 19

y - x = 7

y = x + 7

Substitution

3 (x+7) + 2x = - 19

3x+21 + 2x = - 19

5x + 21-21 = - 19-21

5x/5 = - 40/5

x = - 8

y = x+7 = - 8+7 = - 1

An integers are sets of whole numbers that are basically negative so 1,2,3,4,5,6,7 integers of these are - 1, - 2, - 3, - 4, - 5, - 6, - 7