(CNN) The election of a new anti-austerity government in Greece is raising questions about how the debt-laden state will satisfy its creditors and citizens weary of cost-cutting measures.

The leader of the left-wing Syriza party, Alexis Tsipras , was sworn in as Greece's new Prime Minister on Monday after forming a coalition with the right-wing Independent Greeks party.

Since 2010, Greece has received bailouts totaling 240 billion euros. In return, the International Monetary Fund, European Commission and European Central Bank demanded tax hikes, a freeze on state pensions, bans on early retirement and deep cuts in government salaries.

Syriza's pledges to try to get some of Greece's colossal debt written off and roll back unpopular austerity measures appealed to exasperated members of the electorate -- even if they potentially jeopardize Greece's place in the eurozone . The party's victory could lead to a dramatic showdown with the debt-laden nation's lenders.

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Syriza's message is one that has also resonated in other southern European countries under the restrictions of international bailouts. Its victory could boost other populist parties, such as Beppe Grillo's anti-euro Five Star Movement in Italy and the Podemos Movement in Spain.

Bigger battle

Declaring victory for Syriza on Sunday after polls showed it winning at least 149 seats in the 300-seat parliament, Tsipras, 40, appeared to brace for a bigger battle.

"We are regaining our lost dignity. ... Now that we are heard by all of Europe, we will fight with the same passion, the same confidence," he told cheering supporters. "So let's go and let's all continue this beautiful and tough fight," he said.

"Greece leaves behind the austerity that ruined it, leaves behind the fear, leaves behind five years of humiliation, and Greece moves forward with optimism and hope and dignity," he told the crowd.

European Central Bank Executive Board member Benoît Cœuré told CNN on Monday that Greece would still have to pay its debt.

"They have to pay; those are the European rules of the game. There is no room for unilateral action in Europe, that doesn't exclude a discussion, for example, on the rescheduling of this debt. But I would like to underline that it's not the ECB's money -- it's the governments' money; it's a discussion between Mr. Tsipras and the European governments."

Chief EU Commission spokesman Margaritis Schinas said it respected the "sovereign choice of the Greek people."

"We are ready to engage with the new government once it is formed. Greece has made remarkable progress in recent years, and we stand ready to continue to assist Greece in addressing the remaining reform challenges," he said.

Outgoing Prime Minister: My conscience is clear

The austerity imposed by Greece's international creditors has cut deep . Unemployment has soared to 28%, and many people who still have jobs have seen drastic decreases in wages, pensions frozen and the retirement age pushed back.

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The governing New Democracy party had pointed to recent improvements in economic indicators as signs that things were getting better.

After conceding defeat Sunday, outgoing Prime Minister Antonis Samaras said his conscience was clear.

"I got a country on the verge of ruin. I was asked to try and save it, and I did it," he said. "Most people did not believe we could stand strong, but we did."

Now, he said, Greece is secure and "slowly walking away from the crisis."

"And more than anything," he said, "I give back a country that is a member of the European Parliament and the euro."

On Monday, the CEO of one of Greece's largest banks, Piraeus, said Syriza was coming to power at a "fortunate time."

"The tide is changing in Europe, the macro is improving in Greece, the European Central Bank is launching an unprecedented easing, and that will have a significant bearing on the fortunes of Greece going forward," Anthimos Thomopoulos said.

"Greece has already gone through massive adjustment, much of the hard work has already been completed, the green shoots of recovery are already there, so this is a great opportunity for Greece, a great opportunity for a new government."

'It's a victory for all the people of Europe'

In his victory speech Sunday, Tsipras noted that Greece's election could have an impact far beyond his country's borders.

"Our victory is, at the same time, it's a victory for all the people of Europe that are fighting against austerity that's ruining the common European future," he said.

But it's unclear how Syriza's plans to renegotiate the bailout would play out.