The larger of two consecutive integers is 7 greater than twice the smaller. find the integers.

The largest integer is y= -5 and the smaller is x=-6

Step-by-step explanation:

Define your variables as:

y: Larger integer

x: Smaller integer

Following the first part of the problem:

y=2x +7 (1)

As the two numbers are consecutive the difference between the large number and the smallest is 1  independetly if they are positive or negative integers so:

y-x = 1 (2)

Simplifying y in (2)

y= 1+x (3)

(3) in (1)

1+x=2x+7

-7+1 = 2x-x

x= -6 (4)

(4) in (3)

y= -6 + 1

y=-5

So the large integer y is -5  and the smaller x is -6

(hint): the answer is in the question.