The total of two numbers is 23. Double the larger number exceeds three times the smaller by sixteen. What are the integers?
Let: x = smaller integer
y = larger integer
Eqn1: x + y = 23
Eqn2: 2y - 3x = 16
Isolate x in Eqn1:
x = -y + 23 Eqn3
Substitute Eqn3 in Eqn2, then solve for y:
2y - 3x = 16
2y - 3(-y + 23) = 16
2y + 3y - 69 = 16
2y + 3y = 16 + 69
5y = 85
y = 85/5
y = 17
Substitute in Eqn3, the solve for x:
x = -y + 23
x = -17 + 23
x = 6
Check using Eqn1:
x + y = 23
6 + 17 = 23
23 = 23 √
