Answers

2014-08-23T17:39:40+08:00
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 √
0