Verified answer

[tex]\displaystyle\bf\\|2x+y-3|+4x^{2} -4xy+y^{2} =0\\\\|2x+y-3|+(2x-y)^{2} =0\\\\|2x+y-3|\geq 0 \ \ \ , \ \ \ (2x-y)^{2} \geq 0 \ \ \Rightarrow \ \ \left \{ {{2x+y-3=0} \atop {2x-y=0}} \right. \\\\\\+\left \{ {{2x+y=3} \atop {2x-y=0}} \right.\\ --------\\4x=3\\\\x=3:4=0,75\\\\y=3-2x=3-2\cdot 0,75=3-1,5=1,5\\\\\\Otvet \ : \ (0,75 \ ; \ 1,5)[/tex]