The phrase "a system that pushes" is correct and usable in written English.
You can use it when describing a system that encourages or promotes certain behaviors, actions, or outcomes.
Example: "The new educational framework is a system that pushes students to think critically and engage more deeply with the material."
Alternatives: "a system that drives" or "a system that encourages".
American and European investment managers are paid bonuses based on how well their funds outperform the leading benchmarks, a system that pushes them to take bolder stakes.
The most gratifying for me has been the overwhelming volume of supportive letters, e-mails, and blog postings from fellow physicians, nurses, and other clinicians who felt that it captured the difficulties they've had struggling against a system that pushes them for quantity over quality and fragments care in ways that are costly and dangerous to patients.
The particular challenges for radwaste require the development of a system that pushes the current limits of information technology (IT).
A system that pushes us forward by telling women (and all minorities for that matter) that "we can do and become anything" while simultaneously holding us back.
This device, which consists of a Piezoelectric system that pushes a rod out of a box.
Apparently NOT 120 decibels, according to Todd Whitworth, who has a large barn full of classic cars and a stereo system that pushes out more that 6,000 watts.
a) £5? b) £10? c) Nothing - you refuse to be part of a patriarchal system that pushes women to smear their faces with such unnecessary muck?
Yet both are falling through the cracks of a cruel system that pushes those caught up in its cogs to breaking point.
One of LIGO's systems responds to minuscule seismic tremors by activating a damping system that pushes on the mirrors with exactly the right counterforce to keep them steady; another monitors for disruptive sounds from passing cars, airplanes, or wolves.
Built in homage to flame-tossing baddie Pyro, the system uses a backpack-rigged fueling system that pushes a ton of propane out juuuuust fast enough that Furze doesn't singe his own digits.
Snaking around the tower is a lazy river system that pushes inner-tube riders through its jungle-type landscape.
