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The phrase "system to show" is correct and usable in written English
It can be used when referring to a mechanism or method designed to display information or results. Example: "We have developed a new system to show real-time data analytics for our users."
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We draw on the example of DePuy Orthopaedics' Articular Surface Replacement (ASR™) hip system to show systemic failure of medical implant governance in the United Kingdom (UK).
"We expect the Islamic system to show an appropriate response to this," he said.
The Springboks launched an unsuccessful appeal and then called for rugby's judicial system to show greater consistency in the application of the law.
12. Tiny epics The Game Boy was the first portable system to show that handheld games could be more than just snack-sized diversions.
Pressure is building inside and outside the justice system to show the results of the investigation, several lawyers close to the investigation said.
Politicians have said plenty about zero tolerance for criminals, and the country has an overcrowded prison system to show for it.
Turn it on any high street and it will use the phone's GPS system to show the discounts on offer at nearby restaurants.
The signal output of such systems actuates red or green LEDs in the camera finder system to show whether the image is sharp or not.
He likes being able to ask his navigation system to "Show me the nearest hospitals", whereupon it calls up a list of nearby facilities.
The document itself, Mr. Personius said, concerned the war in Chechnya, and he presented the judge with an elaborate indexing system to show that the enemies referred to were Russians, not Americans.
In November the ABI said estate agents, property websites and developers of new homes should use a traffic light system to show would-be buyers how susceptible to flooding a home is.
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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