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

Directions: Define 2 variables, write 2 equations, and solve the system of equations.
The North Ridgeville Football team played a game against Avon last week. A total of 125 points were scored by both teams. The teams scored a total of 22 six-point touchdowns and three-point field goals. In additon, there were 4 two-point safeties and 12 one-point kids scored. How many touchdowns and field goals were scored by the teams during the game?
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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,
$125=6x+3y+4×2+12×1$
$⇒6x+3y=105$
$⇒2x+y=35$
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:
$13+y=22⇒y=9$
Thus, 13 touchdowns and 9 field goals were scored by the teams.