Final answer:
To solve this problem using the elimination method, assign variables to the number of runs scored by each team. Then write equations based on the given information and solve them using the elimination method. The correct answer is A) Home team scored 14 runs, and the other team scored 16 runs.
Step-by-step explanation:
To solve this problem using the elimination method, let's assign variables to the number of runs scored by each team. Let's say the number of runs scored by the home team is H, and the number of runs scored by the other team is O.
We know that the total number of runs is 30, so we can write the equation H + O = 30. We also know that the other team scored 2 runs more than the home team, so we can write the equation O = H + 2.
Now we can solve these equations using the elimination method:
Substitute the value of O from the second equation into the first equation: H + (H + 2) = 30.
Combine like terms: 2H + 2 = 30.
Subtract 2 from both sides: 2H = 28.
Divide both sides by 2: H = 14.
Substitute the value of H back into one of the original equations to solve for O: O = 14 + 2 = 16.
Therefore, the correct answer is A) Home team scored 14 runs, and the other team scored 16 runs.