2 Zadania algebraiczne

[Redorianin]

1.Oblicz wartość wyrażenia \(\frac{5x^5 (2x^3y^4)^2}{25(x^3y)^3xy^6}\) dla x= 555 i y= 4.

2. Rozwiąż układ równań:
\(\{4(2x + 3) - 2(4y - 1) = 30\\ \frac{5x + 1}{3} - \frac{y - 3}{4} = 3\)

[anka]

1.\(\frac{5x^5 (2x^3y^4)^2}{25(x^3y)^3xy^6}=\frac{x^5 2^2x^6y^8}{5x^9y^3xy^6}=\frac{4x^{11} y^8}{5x^{10}y^9}=\frac{4x}{5y}\)
Podstawiasz i liczysz

2.
\(\{4(x + 3) - 2(4y - 1) = 30\\ \frac{5x + 1}{3} - \frac{y - 3}{4} = 3\)
\(\{4x + 12 - 8y +2 = 30\\ \4(5x + 1) - 3(y - 3) = 36\)
\(\{4x - 8y = 30-12-2\\ 20x + 4 - 3y +9 = 36\)
\(\{4x - 8y = 16 \\ 20x - 3y = 36-4-9\)
\(\{4x - 8y = 16 \ / \cdot (-5)\\ 20x - 3y = 23\)
\(\{-20x +40y = -80\\ 20x - 3y = 23\)
dodajemy stronami
\(37y=-57 \ /:37\)
\(y=- \frac{57}{37}\)
\(\{4x - 8y = 16 \ /:4\\y=- \frac{57}{37}\)
\(\{x - 2y = 4\\y=- \frac{57}{37}\)
\(\{x - 2 \cdot(- \frac{57}{37}) = 4\\y=- \frac{57}{37}\)
\(\{x= \frac{34}{37} \\y=- \frac{57}{37}\)