Rozwiązane

Rozwiąż układ równań
2x+3y= 20
-3x+5y= -5



Odpowiedź :

Magda

Odpowiedź:

[tex]\begin{cases}2x+3y=20\ \ /*3\\-3x+5y=-5\ \ /*2\end{cases}\\\\\\+\begin{cases}6x+9y=60\\-6x+10y=-10\end{cases}\\----------\\19y=50\ \ /:19\\\\y=\frac{50}{19}\\\\\\2x+3*\frac{50}{19}=20\\\\2x+\frac{150}{19}=20\\\\2x=20-\frac{150}{19}\\\\2x=\frac{380}{19}-\frac{150}{19}\\\\2x=\frac{230}{19}\ \ /:2\\\\x=\frac{\not230^1^1^5}{19}*\frac{1}{\not2_{1}}\\\\x=\frac{115}{19}\\\\\\\begin{cases}x=\frac{115}{19}\\y=\frac{50}{19}\end{cases}[/tex]

Krysia

[tex]\begin{cases}2x+3y= 20\ \ |*3\\-3x+5y= -5\ \ |*2 \end{cases}\\\\\begin{cases}6x+9y= 60\\-6x+10y= -10\end{cases} \\+---------\\19y=50\ \ |:19\\y=\frac{50}{19}\\\\2x+3y= 20\\2x=-3x+20\ \ |:2\\\\x=-\frac{3}{2}y+10\\\\x=-\frac{3}{\not{2}^1}*\frac{\not{50}^{25}}{19}+10=-\frac{75}{19 }+10= -\frac{75}{19 }+ \frac{190}{19}=\frac{115}{19}[/tex]

[tex]\begin{cases}x= \frac{115}{19} \\ y=\frac{50}{19} \end{cases}[/tex]

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