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,

\(\displaystyle{125}={6}{x}+{3}{y}+{4}\times{2}+{12}\times{1}\)

\(\displaystyle\Rightarrow{6}{x}+{3}{y}={105}\)

\(\displaystyle\Rightarrow{2}{x}+{y}={35}\)

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.

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,

\(\displaystyle{125}={6}{x}+{3}{y}+{4}\times{2}+{12}\times{1}\)

\(\displaystyle\Rightarrow{6}{x}+{3}{y}={105}\)

\(\displaystyle\Rightarrow{2}{x}+{y}={35}\)

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.