Let x be the number of dinner tickets sold by Kimberly and y be the number of dessert tickets sold by Kimberly.
According to the problem, Kimberly sold a total of 100 tickets, so we have:
x + y = 100
According to the problem, Kimberly collected a total of $900, so we have:
10x + 6y = 900
This is because the cost of each dinner ticket is $10 and Kimberly sold x dinner tickets, so she collected 10x dollars from dinner ticket sales. Similarly, the cost of each dessert ticket is $6 and Kimberly sold y dessert tickets, so she collected 6y dollars from dessert ticket sales.
Therefore, the system of equations for this problem is:
x + y = 100
10x + 6y = 900
This system can be solved using various methods, such as substitution or elimination, to find the values of x and y that satisfy both equations.