Question

A number added to five times the second number is 36. The first number decreased by twice the second number is 1. Find the two numbers.

Answer 1

Let x be the first, number and y be the second, then we can set the following system of equations:

`\begin{gathered} x+5y=36, \\ x-2y=1. \end{gathered}`

Subtracting the second equation from the first one, and solving for y we get:

`\begin{gathered} x+5y-x+2y=36-1, \\ 7y=35, \\ (7y)/(7)=(35)/(7), \\ y=5. \end{gathered}`

Substituting y=5 in the second equation, and solving for x we get:

`\begin{gathered} x-2(5)=1, \\ x=1+10, \\ x=11. \end{gathered}`

Answer: The first number is 11 and the second one is 5.