Answer:
The winning ticket is: A. [tex]x^2-3xy+4-2x^2=-x^2-2xy-xy+4[/tex].
Step-by-step explanation:
We have been given that Tomas’s math class held a raffle. The student who picked the ticket with a pair of equivalent equations on it would win.
Let us check our given pairs of equations one by one.
A. [tex]x^2-3xy+4-2x^2=-x^2-2xy-xy+4[/tex]
Let us combine like terms on the both sides of our equation.
[tex](x^2-2x^2)-3xy+4=-x^2-(2xy+xy)+4[/tex]
[tex](-x^2)-3xy+4=-x^2-(3xy)+4[/tex]
[tex]-x^2-3xy+4=-x^2-3xy+4[/tex]
We can see that both sides of our equation are equal, therefore, option A is the correct choice.
B. [tex]7y^2-yz+4-2yz=7y^2-2yz+4yz[/tex]
Let us combine like terms on the both sides of our equation.
[tex]7y^2-(yz+2yz)+4=7y^2-(2yz-4yz)[/tex]
[tex]7y^2-(3yz)+4=7y^2-(-2yz)[/tex]
[tex]7y^2-3yz+4\neq 7y^2+2yz[/tex]
Since the both sides of our equation are not equal, therefore, option B is not a correct choice.
C. [tex]3a^2-ab+3-3ab=6a^2-2ab+3-2ab[/tex]
Upon combining like terms we will get,
[tex]3a^2-(ab+3ab)+3=6a^2-(2ab+2ab)+3[/tex]
[tex]3a^2-(4ab)+3=6a^2-(4ab)+3[/tex]
[tex]3a^2-4ab+3\neq 6a^2-4ab+3[/tex]
Since the both sides of our equation are not equal, therefore, option C is not a correct choice.
D. [tex]9s^2-st+5-3st=6s^2-3st+5+3s^2[/tex]
Upon combining like terms we will get,
[tex]9s^2-(st+3st)+5=(6s^2+3s^2)-3st+5[/tex]
[tex]9s^2-(4st)+5=(9s^2)-3st+5[/tex]
[tex]9s^2-4st+5\neq 9s^2-3st+5[/tex]
Since the both sides of our equation are not equal, therefore, option D is not a correct choice.
