Rozwiąż algebraicznie układ równań.... Question from @bloodyprincess005

November 2018 1 25 Report

Rozwiąż algebraicznie układ równań. $\left \{ {{4x-4y=1} \atop {-2x-8y=-3}} \right.$ $\left \{ {{\frac{1}{2}x+\frac{1}{3}y=5} \atop {\frac{1}{2}x+\frac{1}{9}y=3}} \right.$ $\left \{ {{-2(x-y)+3(2x-y)=3} \atop {3(x+y)+2(x-y)=15}} \right.$

Zgłoś nadużycie!

$\left \{ {{-2(x-y)+3(2x-y)=3} \atop {3(x+y)+2(x-y)=15}} \right$

$\begin{cases}-2x+2y+6x-3y=3\\ 3x+3y+2x-2y=15\end{cases}$

$\begin{cases}4x-y=3\\5x+y=15\end{cases}$
+___________
$9x=18$

$x=2$

$\begin{cases}x=2\\5x+y=15\end{cases}$

$\begin{cases}x=2\\5\cdot 2+y=15\end{cases}$

$\begin{cases}x=2\\10+y=15\end{cases}$

$\begin{cases}x=2\\y=15-10\end{cases}$

$\begin{cases}x=2\\y=5\end{cases}$

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$\left \{ {{4x-4y=1} \atop {-2x-8y=-3\ /\cdot 2}} \right$

$\begin{cases} 4x-4y=1\\ -4x-16y=-6\end{cases}$
+_________________
$-20y=-5$

$y=\frac{1}{4}$

$\begin{cases} 4x-4y=1\\ y= \frac{1}{4} \end{cases}$

$\begin{cases} 4x-4\cdot \frac{1}{4} =1\\ y= \frac{1}{4}\end{cases}$

$\begin{cases} 4x-1=1\\ y= \frac{1}{4}\end{cases}$

$\begin{cases} 4x=1+1\\ y= \frac{1}{4}\end{cases}$

$\begin{cases} 4x=2\\ y= \frac{1}{4}\end{cases}$

$\begin{cases} x= \frac{1}2{} \\ y= \frac{1}{4}\end{cases}$

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$\left \{ {{\frac{1}{2}x+\frac{1}{3}y=5\ / \cdot 6} \atop {\frac{1}{2}x+\frac{1}{9}y=3\ / \cdot 18}} \right$

$\begin{cases} 3x+2y=30\\ 9x+2y=54\ /\cdot (-1)\end{cases}$

$\begin{cases} 3x+2y=30\\ -9x-2y=-54\end{cases}$
+_____________
$-6x=-24$

$x=4$

$\begin{cases} x=4\\3x+2y=30\end{cases}$

$\begin{cases} x=4\\3\cdot 4+2y=30\end{cases}$

$\begin{cases} x=4\\12+2y=30\end{cases}$

$\begin{cases} x=4\\2y=30-12\end{cases}$

$\begin{cases} x=4\\2y=18\end{cases}$

$\begin{cases} x=4\\y=9\end{cases}$