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Let's set up the system of equations to solve for the number of adult (x) and student (y) tickets sold:
Equation 1: x = y + 50 (since there were 50 more adult tickets sold compared to student tickets)
Equation 2: 5x + 2y = 950 (the total amount collected from selling adult and student tickets was $950)
To solve this system of equations, we can substitute the value of x from equation 1 into equation 2:
5(y + 50) + 2y = 950
5y + 250 + 2y = 950
7y + 250 = 950
7y = 700
y = 100
Substituting the value of y back into equation 1:
x = 100 + 50
x = 150
Therefore, there is only one solution to this system of equations.