Question

There are two numbers, which sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers

Answer 1

Let "n" be the smaller number, then
the larger number = 3n-19

n + 3n - 19 = 53
4n = 53 + 19
4n = 72
n = 72/4
n = 18  ←  smaller number

larger number = 53 - 18 = 35

Answer: 18 and 35.

Answer 2

x + y = 53.
Let x be the smaller number; then it'll be 3x = 19 + y

Set the first equation equal to x, then substitute the values and solve.
x + y = 53.
x = 53 - y.
3(53 - y) = 19 + y
x = 18; y = 35
140 - y = y
y = 70.

53 - 70 = -17
x = -17; y = 70.
-17 + 70 = 53;