"build up a system" is correct and can be used in written English.
You can use it when you want to talk about constructing or putting together a system for a certain reason. For example, "We must build up a system to make sure that all of our customers have an satisfactory experience."
We build up a system of public structures like courts, laws, schools, roads, bridges -- spending -- that enable commerce to prosper.
What else? Another question looked trickier at first glance: "Sticking to the Party's overall leadership and coordination among different sectors, to build up a system with the Party's full leadership role, and guarantee that the Party's leadership is carried out in domains such as (blank), (blank), and (blank)".
Omitting other relevant factors is perhaps inevitable if one is trying to build up a system of positive myths about capitalism, but what Mr. Berger leaves out of his analysis is a realization that capitalism has some defects as well as some virtues.
And try to build up a system that will enable us to get information quickly, to respond to it quickly.
Gaggle is now employed in the integration of databases over the Internet in the US Department of Energy's effort to build up a systems biology knowledgebase [ 78].
But they have also built up a system of incentives to ensure employees meet existing goals.
I like the idea that it builds up a system of better preschools.
Moreover, the city has built up a system of banks, advisers, specialized analysts and investors, lawyers, publicists and accountants around natural resources businesses.
This duty can be enforced by the donee beneficiary for his own benefit". "A promise to discharge the promisee's duty [to another person] creates a duty of the promisor to the creditor beneficiary to perform the promise". Around these statements is built up a system of other rules governing the relations of the beneficiary with both the promisor and the promisee.
In addition to this, the company has built up a system for managing interactive seating charts and running affiliate marketing programmes, so that third parties can also link up with its ticketing system.
"We have built up a system that seems to mostly benefit the system itself, the employees or possibly those in power".
