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