In a football game, Team A defeated Team B by a score of 31 to 14. The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3
points, respectively. The numbers of touchdowns and extra-point kicks were equal. There were six times as many touchdowns as field goals. Find the number of touchdowns, extra-point
kicks, and field goals scored.

The number of touchdowns is 4.The number of extra-point kicks is 4.and the number of field goals is 2.What are linear equations in three variables?If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.How to solve the system of linear equations in three variables?Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".Total points scored in game = 20+14 =34Now, According to the given question,                                 6x + y + 3z = 34 -----------(I)                                 x = y ----------(II)                                 x = 2z                                 z = [tex]\frac{x}{2}[/tex] -----------(III)Putting the values of "y" and "z" in equation (I), we get                               6x + x + 3×[tex]\frac{x}{2}[/tex] = 34                                [tex]\frac{17x}{2}[/tex] = 34                                x = 4Now, putting the value of "x" in equations (II) and (III), we get                                y = 4.                                z = 2.Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.To learn more about the system of linear equations, visit:https://brainly.com/question/26150814#SPJ1