Is it correct to use variables that are not not quantified in my statement?

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I want to find the truth value of this statement given that the domain of discourse is $\mathbb Z$:

$$∃m∃n (2x+5y=y ∧ x+5y=3).$$

I am a bit confused whether the statement is correct or not since $x$ and $y$ are not quantified (we did not say $∃x$ or $∀x$). If it is correct not to quantify them, then we can deduce that the statement is true for $x=-2$ and $y=1.$ But I am unsure if this is the right way to solve this problem.