Directions: Define 2 variables, write 2 equations, and solve the system of equations. The North Ridgeville Football team played a game against Avon la

Step 1
Let x and y denote the number of touchdowns and field goals were scored by the teams during the game.
Given that:
Total touchdowns and field goals scored = 22
x + y = 22
Total score = Total scores of touchdowns, field goals and additional points, that is,
${\displaystyle 125=6x+3y+4\times 2+12\times 1}$
${\displaystyle \Rightarrow 6x+3y=105}$
${\displaystyle \Rightarrow 2x+y=35}$
Step 2
Therefore, the system of equations to solve is:
x+y=22
2x+y=35
First, eliminate y.
Subtract first equation from the second equation to get
x = 13
Step 3
Solve for y by substituting the value for x in either of the two equations:
${\displaystyle 13+y=22\Rightarrow y=9}$
Thus, 13 touchdowns and 9 field goals were scored by the teams.