[tex]\displaystyle\\\text{Notatii:}\\~~~~~~~x = \text{pretul unui stilou}\\~~~~~~~y = \text{pretul unui pix}\\\\\text{Procente:}\\~~~~~~~\text{Stiloul se ieftineste cu }~10\%~\text{si ajunge la:}\\~~~~~~~~~~~~~~x - 10\% \times x = x -\frac{10}{100}\times x=x-0,\!1\times x=x(1-0,\!1) =0,\!9x\\\\~~~~~~~\text{Pixul se scumpeste cu }~20\%~\text{si ajunge la:}\\~~~~~~~~~~~~~~y + 20\% \times y = y +\frac{20}{100}\times y=y+0,\!2\times y=y(1+0,\!2) =1,\!2y\\\\\text{Scriem sistemul de ecuatii:}[/tex]
[tex]\begin{cases}x-y=10~~~~~~\implies \text{substitutia:}~~~\boxed{x=10+y}\\0,9x-1,\!2y=6 \end{cases}\\\\\\0,\!9(10+y)-1,\!2y=6\\9+0,\!9y-1,\!2y=6\\9-0,\!3y=6\\-0,\!3y=6-9\\-0,\!3y=-3~~~\Big|\times(-1)\\0,\!3y=3\\y=\frac{3}{0,\!3}\\\boxed{\bf y=10~Lei~un~pix}\\\\\text{\bf Ne intoarcem la substitutie.}\\x=10+y=10+10\\\boxed{\bf x=20~Lei~un~stilou}[/tex]
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