Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 14x + 15, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 9x + 55.
Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?
4 weeks
8 weeks
23 weeks
70 weeks
To find when their savings accounts will have the same amount of money, we need to find the value of x when y is the same in both equations.
So, we set 14x + 15 = 9x + 55 and solve for x:
14x + 15 = 9x + 55
5x + 15 = 55
5x = 40
x = 8
Therefore, after 8 weeks, both siblings' savings accounts will have the same amount of money.
So, the correct answer is: 8 weeks.