How exactly do i start this equation, and how do i solve it

Question

In a football game, Team A defeated Team B by a score of 31 to 17. The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3 points, respectively. The numbers of touchdowns and extra-point kicks were equal. There were three times as many touchdowns as field goals. Find the number of touchdowns, extra-point kicks, and field goals scored.

Answer 1

6T + E + 3F = 31+17 = 48

T=3F, F=T/3

T=E

6T + T + 3(T/3) = 48

8T = 48

T =48/8 = 6 touchdowns

E=T = 6 extra points

F =T/3 = 2 field goals

6(6)+6 +3(2) = 36 +6+ 6 = 48 total points