The correct set of inequalities are - [tex]3x^{2} > y[/tex] and [tex]y^{2}+6 > x[/tex].
We have three times the square of a number is greater than a second number and the square of the second number increased by 6 is greater than the first number.
We have to find which system of inequalities mentioned represents this situation.
What is an inequality?
An inequality is mathematical relation which compares two or more mathematical expressions.
In the question, it is given that -
Three times the square of a number is greater than a second number. Let the first number be [tex]x[/tex] and the second number be [tex]y[/tex].
According to question -
[tex]3x^{2} > y[/tex]
and - the square of the second number increased by 6 is greater than the first number. We can write this statement mathematically as -
[tex]y^{2}+6 > x[/tex]
Hence, the correct set of inequalities are - [tex]3x^{2} > y[/tex] and [tex]y^{2}+6 > x[/tex]
To solve more questions on inequalities, visit the link below -
https://brainly.com/question/20383699
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