What is the smallest number?

Question

The sum of two numbers is 34. The difference of those same two numbers is 16.

Problem : X + Y = 34

X + y = 16

Answer 1

X + Y = 34 "The sum of two numbers is 34"

X - Y = 16 "The difference of those same two numbers is 16.

--------------- [add equations; elimination is easier than substitution]

2X = 50

X = 25

Y = 9 [this is the smaller of the two numbers]

Check:

25 + 9 = 34

25 - 9 = 16

Answer 2

No

x + y = 34

x - y = 16

add y drops out

find x then substitute in for x and solve for y

x = 25

y = 9