In the last quarter of a high school football game, your team i s behind by 21 points. A field goal is worth 3 points and a touchdown (after the extra point is worth 7 points. Let x represent the number of field goals scored and y represent the number of touchdowns scored. Write an inequality that models the different number of field goals and touchdowns your team could score to win the game. (Assume the other team doesn't score any more points.)

3x + 7y > 21

Step-by-step explanation:

3x + 7y > 21

where:

x = number of field goals needed to win

y = number of touchdowns (plus extra point) needed to win

Since your team is 21 points behind and you want to win the game, not tie it, the number of field goals and touchdowns must result in a number higher than 21, not equal to or higher than.

3x + 7y > 21

3x + 7y > 21

where:

x = number of field goals needed to win

y = number of touchdowns (plus extra point) needed to win

Since your team is 21 points behind and you want to win the game, not tie it, the number of field goals and touchdowns must result in a number higher than 21, not equal to or higher than.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is