The sum of two numbers is 53. if twice the first number minus three times the second number is 26, find both numbers.

Make an equation system based on the problem
eg. a is the first number and b is the seond number
An equation for "The sum of two numbers is 53" is
⇒ a + b = 53
An equation for "twice the first number minus three times the second number is 26"
⇒ 2a - 3b = 26

Solve the equations by elimination and subtitution method
Eliminate a to find the value of b
a + b = 53   (multiplied by 2)
2a - 3b = 26

2a + 2b = 106
2a -  3b = 26
- (substract)
       5b = 80
         b = 80/5
         b = 16

Subtitute the value of b to one of the equations
a + b = 53
a + 16 = 53
a = 53 - 16
a = 37

The numbers are 16 and 37