Question

решите систему уравнений способом сложения​

Answer 1

$1.\;\begin{cases}5x+y=20\\2x-y=1\end{cases}\Rightarrow\begin{cases}5x+y+2x-y=20+1\\5x-y=1\end{cases}\Rightarrow\\\Rightarrow\begin{cases}7x=21\\y=2x-1\end{cases}\Rightarrow\begin{cases}x=3\\y=5\end{cases}\\\\\\2.\;\begin{cases}2x-3y=9\\4x+3y=27\end{cases}\Rightarrow\begin{cases}2x-3y+4x+3y=9+27\\4x+3y=27\end{cases}\Rightarrow\\\Rightarrow\begin{cases}6x=36\\y=9-\frac43x\end{cases}\Rightarrow\begin{cases}x=6\\y=1\end{cases}$

$3.\;\begin{cases}2x+3y=2\\-2x+5y=-18\end{cases}\Rightarrow\begin{cases}2x+3y=2\\-2x+5y+2x+3y=-18+2\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x=2-\frac32y\\8y=-16\end{cases}\Rightarrow\begin{cases}x=5\\y=-2\end{cases}\\\\4.\;\begin{cases}x+4y=39\\2x-y=15\;\;\;\times4\end{cases}\Rightarrow\begin{cases}x+4y=39\\8x-4y=60\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x+4y+8x-4y=39+60\\y=2x-15\end{cases}\Rightarrow\begin{cases}x=11\\y=7\end{cases}$