Final answer:
Each girl scored 2 points and each boy scored 0 points.
Step-by-step explanation:
Let's assume that each girl scored x points and each boy scored y points. We are given that 8 girls and 7 boys scored a total of 98 points, so we can set up the equation: 8x + 7y = 98. We are also given that the difference between the number of points scored by the girls and boys is 14, so we can set up another equation: 8x - 7y = 14.
Solving these two equations simultaneously, we can use the method of elimination. Multiply the first equation by 7 and the second equation by 8, which gives us 56x + 49y = 686 and 64x - 56y = 112. Now, subtract the second equation from the first equation to eliminate y: (56x + 49y) - (64x - 56y) = 686 - 112. Simplifying, we get -8x + 105y = 574.
Now we have a system of two equations: -8x + 105y = 574 and 8x - 7y = 14. Multiply the second equation by -105 to get -840x + 735y = -1470. Now, we can add this equation to the first equation to eliminate x: (-8x + 105y) + (-840x + 735y) = 574 + (-1470). Simplifying, we get 840y = -896. Dividing by 840, we find y = -1.067. Since we cannot have a negative number of points, we round y to the nearest whole number, which is 0. Now, substitute y = 0 back into the second equation to find x: 8x - 7(0) = 14. Simplifying, we get 8x = 14 and dividing by 8, we find x = 1.75. Again, we round to the nearest whole number, which is 2.
Therefore, each girl scored 2 points and each boy scored 0 points.
Learn more about scoring points in a team