Find two consecutive integers such that 4 times the larger exceeds 3 times the smaller by 23.

Let x and y be the integers

we are told that 4x = 3y + 23  EQN (1)

and x = y + 1  EQN (2)

We have two unknowns and two equations meaning we can solve this system.

Substituting (2) into (1) we get 

4(y+1) = 3y + 23

which solves to y = 19 which in turn means x = 20

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !