4.3 system of linear equations

Question

one number is five less than a second number. Three times the first is 6 more than 6 times the second. Find the numbers. 

Answer 1

Let F be the 1st number, S the 2nd.

First condition: F = S - 5

Second condition: 3F = 6S + 6

 

Substituting for F:   3(S - 5)= 6S + 6

Expanding:            3S - 15 = 6S + 6

Solving:                 3S - 6S = 6 + 15

                                 -3S =21

                                   S = -7

                                  F = -12