USWNT downs Iceland in Algarve
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The Americans took the lead thanks to an own goal by Sif Altadottir, who deflected a Meghan Schnur cross into the net.
Cheney broke clear a minute later and extended the U.S. advantage. The forward, who had earlier missed several clear chances, took a pass from Lori Lindsey and struck her shot into the right-hand corner for her fifth international goal.
"I had plenty of opportunities but I knew I had to keep going," Cheney said.
The U.S., a six-time Algarve champion, struggled to take control of the game but Solo kept a clean sheet with penalty saves after 12 minutes and in injury time, both times diving to her right.
"I think Hope is the best," U.S. coach Pia Sundhage said. "I felt we picked up our rhythm during the game."
Solo admitted she had never saved two penalties in one match. "I was more doubtful about the second one," she said.
The U.S., which has won the title in southern Portugal six times in the past nine years, meets Norway in the second batch of round-robin games on Friday.
Sweden, which beat the Americans in last year's final, and four-time Algarve champion Norway were playing later Wednesday in Group B's other game.
In Group A, Finland drew 1-1 with two-time Algarve champion China. Two-time world champion Germany was taking on Denmark later in the same group.
The winner of each group will meet in the final on March 11.