Answer: Choice A
6x+3y = 15
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Work Shown:
x = number of touchdowns
y = number of field goals
6x = points only from the touchdowns (ignore the fieldgoals for now)
3y = points only from the field goals (ignore the touchdowns for now)
6x+3y = total number of points from both categories combined
6x+3y = 15 since Kingston scored 15 points overall
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Extra info (optional section)
We don't have enough info to fully nail down what x and y are in terms of numbers, but let's say he scored y = 1 field goal.
Then x would be,
6x+3y = 15
6x+3(1) = 15
6x+3 = 15
6x = 15-3
6x = 12
x = 12/6
x = 2
This tells us that Kingston scored 2 touchdowns if he scored 1 field goal.
2 touchdowns + 1 field goal = 2*6 + 1*3 = 12 + 3 = 15 points total
The ordered pair (x,y) = (2,1) is one solution to that equation.
Another solution is (x,y) = (1,3) following similar steps as shown above.
The third solution is (x,y) = (0,5). Each time x goes down by 1, y goes up by 2 and vice versa.
We only have 3 solutions in this case because x & y are nonnegative whole numbers. If x and/or y were allowed to be any real number, then we'd have infinitely many solutions.
