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The phrase "a system that exists" is correct and usable in written English.
You can use it when discussing the presence or reality of a particular system, often in a technical or theoretical context.
Example: "In our research, we focused on a system that exists within the framework of quantum mechanics."
Alternatives: "a system in place" or "an existing system".
Exact(6)
One point that the law does not settle is how individuals can supply energy to the grid, a system that exists in other countries.
Our failure to give any value to the last phase of life, our insistence on health and safety above all, has led to a dependence on care homes that are little more than parking places; Gawande is rightly scathing about a system that exists largely as a form of containment, where the temptation is to deal with people as if they are inconvenient.
But he wondered whether a life spent in the U.N., a system that exists in the name of principle yet survives by compromise, might not be especially cooling, and he said of Annan, "Remember that he spent from 1962 — forty years — in the machine, and he has been a consummate user of the machine as well as being part of it".
There is a system that exists to help invalidate those issues, and it's far from perfect.
"It turns out," says Narula, "that anyone who wants to ask a 'What if' question about a system that exists in the real world needs to run these kind of simulations".
"What remains is the status quo: years and years of appeals and billions of dollars to prop up a system that exists in name only," said Ana Zamora, criminal justice policy director for the ACLU of Northern California and a death penalty opponent.
Similar(53)
What [the film is] asking for is to go back to a system that existed before.
It's a system that existed informally in hospitals around the country before 1980.
"This bill addressed a structural problem in a system that existed for many years," Mead said in a statement.
"There's a whole system that exists in our society if a mistake is made and a patient has been harmed," Gupta told CNN last month.
Clearly, a health system that exists to take in money rather than to benefit human health is not good for diabetics.
More suggestions(16)
a system that constitutes
a mechanism that exists
a computer that exists
a model that exists
a system that already exists
a system that existed
a system that presents
a system that exhibits
a system that appears
a reality that exists
a system that places
a system that lacks
a system that contains
a system that lets
a system that is
a system that uses
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com