Let x be a larger number and y be a smaller number.
Given that the larger of two numbers is 10 less than twice the smaller number.
x = 2y - 10
We also have the of the two numbers is 38.
x + y = 38
We will use substitution method to solve the system of linear equations. Plug in the x-value from the 1st equation into the 2nd equation to find y.
(2y - 10) + y = 38 ⇒ 2y - 10 + y = 38 ⇒ 3y - 10 = 38 ⇒ 3y = 48 ⇒ y = 16
Plug in 16 for y in one of the original equations to solve for x. We get
x + 16 = 38 ⇒ x = 22 or x = 2(16) - 10 = 32 - 10 = 22
The two numbers are 16 and 22. 16 is a smaller number and 22 is a larger number.
