ODP:

I - D

II - A

III - B

IV - C

 

Rozwiązujemy układ I:

$\{\begin{array}{l}x-2y=1\mid +2y\\ 2x-y=5\end{array}$

$\{\begin{array}{l}x=1+2y\\ 2\left(1+2y\right)-y=5\end{array}$  

$\{\begin{array}{l}x=1+2y\\ 2+4y-y=5\mid -2\end{array}$  

$\{\begin{array}{l}x=1+2y\\ 3y=3\mid :3\end{array}$  

$\{\begin{array}{l}x=1+2y\\ y=1\end{array}$  

$\{\begin{array}{l}x=1+2\cdot 1\\ y=1\end{array}$  

$\{\begin{array}{l}x=3\\ y=1\end{array}$  

 

Rozwiązujemy układ II:

$\{\begin{array}{l}y=\frac{1}{2}x\\ x+y=6\end{array}$  

$\{\begin{array}{l}y=\frac{1}{2}x\\ x+\frac{1}{2}x=6\end{array}$  

$\{\begin{array}{l}y=\frac{1}{2}x\\ \frac{3}{2}x=6\mid \cdot \frac{2}{3}\end{array}$  

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

$\{\begin{array}{l}y=\frac{1}{2}\cdot 4\\ x=4\end{array}$  

$\{\begin{array}{l}y=2\\ x=4\end{array}$        

 

Rozwiązujemy układ II:

$\{\begin{array}{l}x=y-3\\ y-2x=5\end{array}$  

$\{\begin{array}{l}x=y-3\\ y-2\left(y-3\right)=5\end{array}$  

$\{\begin{array}{l}x=y-3\\ y-2y+6=5\mid -6\end{array}$  

$\{\begin{array}{l}x=y-3\\ -y=-1\mid \cdot \left(-1\right)\end{array}$   

$\{\begin{array}{l}x=y-3\\ y=1\end{array}$  

$\{\begin{array}{l}x=1-3\\ y=1\end{array}$  

$\{\begin{array}{l}x=-2\\ y=1\end{array}$  

 

Rozwiązujemy układ IV:

$\{\begin{array}{l}2x-y=1\\ y=-4x-7\end{array}$  

$\{\begin{array}{l}2x-\left(-4x-7\right)=1\\ y=-4x-7\end{array}$   

$\{\begin{array}{l}2x+4x+7=1\mid -7\\ y=-4x-7\end{array}$  

$\{\begin{array}{l}6x=-6\mid :6\\ y=-4x-7\end{array}$  

$\{\begin{array}{l}x=-1\\ y=-4\cdot \left(-1\right)-7\end{array}$  

$\{\begin{array}{l}x=-1\\ y=-3\end{array}$