Question

In a football game, a touchdown with an extra point is worth 7 points and a field goal is worth 3 points. Suppose that in a game the only scoring done by teams are touchdowns with extra points and field goals

a. Which of the scores 1 to 25 are impossible for a team to score?​

Answer 1

Allow x to equal the number of touchdowns, and y to equal the number of field goals.

2

7x+3y=26

Touchdowns, x, are seven points each, and field goals, y, are 3 points each. The total points must equal 26.

3

x= -y+6

Solve for x or y. I chose x.

4

7(-y+6)+3y=26

Substitute that for x in the other eqaution.

5

-7y+42+3y=26

Distribute.

6

-4y+42=26

Combine like terms.

7

-4y= -16

Isolate the variable, so subtract 42 from both sides.

8

y= 4

Divide by -4

9

x+4=6

Substitute.

10

x=2

Subtract 4 from both sides.

RESULT

(2,4)