Let x and y denote the number of touchdowns and field goals were scored by the teams during the game.
Total touchdowns and field goals scored = 22
x + y = 22
Total score = Total scores of touchdowns, field goals and additional points, that is,
Therefore, the system of equations to solve is:
First, eliminate y.
Subtract first equation from the second equation to get
x = 13
Solve for y by substituting the value for x in either of the two equations:
Thus, 13 touchdowns and 9 field goals were scored by the teams.