Using a system of equations, the three consecutive integers are given as follows:
20, 21 and 22.
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the consecutive integers are given by:
x, x + 1 and x + 2.
The sum of the second and third exceeds half of the first by 33, hence:
x + 1 + x + 2 = 0.5x + 33
2x + 3 = 0.5x + 33
1.5x = 30
x = 30/1.5
x = 20.
Hence the integers are 20, 21 and 22.
More can be learned about a system of equations at
https://brainly.com/question/24342899
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