In the county championship football game, the Falcons and the Spartans scored a total of 62 points. The points came from a total of 17 different scoring plays, which
were a combination of touchdowns, field goals, safeties, and extra-point kicks, worth
6,3,2, and 1 points, respectively. The sum of the number of extra-point kicks and
field goals equaled the number of touchdowns. There were 2 times as many field
goals as safeties.
a. Write a system of equations that represents the given information. Describe what
each variable in the system represents.
b. Write the system of equations from part (a) as a matrix equation AX = B.
c. Use an inverse matrix to solve the system of equations. How many touchdowns,
field goals, extra-point kicks, and two-point conversions were scored during
the game?