Question

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

Answer 1

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