let

y = the age of Yuri

z = the age of Zack

Yuri is twice as old as Zack

y = 2z divide both sides by 2

z = y/2

Four years from now, the sum of their ages will be 23

(y + 4) + (z + 4) = 23

plug z = y/2 into the last equation

(y + 4) + (y/2 + 4) = 23

we find

y = 10 years

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Yuri is 10 years old.