$\text{a)}$  

$\{\begin{array}{l}-\left(x+4y\right)+2=y-x+17\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}-x-4y+2=y-x+17\mid +x\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}-4y+2=y+17\mid -y\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}-5y+2=17\mid -2\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}-5y=15\mid :\left(-5\right)\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}y=-3\\ 8x-y=3\end{array}$  

$\{\begin{array}{l}y=-3\\ 8x-\left(-3\right)=3\end{array}$  

$\{\begin{array}{l}y=-3\\ 8x+3=3\mid -3\end{array}$  

$\{\begin{array}{l}y=-3\\ 8x=0\mid :8\end{array}$  

$\{\begin{array}{l}y=-3\\ x=0\end{array}$  

$\{\begin{array}{l}x=0\\ y=-3\end{array}$  

---

$\text{b)}$  

$\{\begin{array}{l}\frac{2x-y}{3}=\frac{3x+y}{2}\mid \cdot 6\\ x=2\left(x+y+1\right)\end{array}$  

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

$\{\begin{array}{l}4x-2y=9x+3y\mid -4x\\ x=2x+2y+2\mid -x\end{array}$  

$\{\begin{array}{l}-2y=5x+3y\mid +2y\\ 0=x+2y+2\mid -2\end{array}$  

$\{\begin{array}{l}0=5x+5y\mid :5\\ -2=x+2y\mid \cdot \left(-1\right)\end{array}$  

$\{\begin{array}{l}0=x+y\\ 2=-x-2y\end{array}$  

Dodajemy do siebie lewe i prawe strony równań.

$+\{\begin{array}{l}0=x+y\\ 2=-x-2y\end{array}$  
_________________________

$2=-y$  

$y=-2$  

Wyznaczamy  $x$ .

$0=x+y$  

$0=x-2\mid +2$  

$2=x$  

Zatem:

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

---

$\text{c)}$  

$\{\begin{array}{l}1-\frac{x-1}{2}=2+\frac{y+1}{3}\mid \cdot 6\\ x+y+4=0\mid -4\end{array}$  

$\{\begin{array}{l}6-3\left(x-1\right)=12+2\left(y+1\right)\\ x+y=-4\end{array}$  

$\{\begin{array}{l}6-3x+3=12+2y+2\\ x+y=-4\end{array}$  

$\{\begin{array}{l}-3x+9=2y+14\mid -2y\\ x+y=-4\end{array}$  

$\{\begin{array}{l}-3x-2y+9=14\mid -9\\ x+y=-4\mid \cdot 2\end{array}$  

$\{\begin{array}{l}-3x-2y=5\\ 2x+2y=-8\end{array}$  

Dodajemy do siebie lewe i prawe strony równań.

$+\{\begin{array}{l}-3x-2y=5\\ 2x+2y=-8\end{array}$  
_________________________

$-x=-3$  

$x=3$  

Wyznaczamy  $y$ .

$x+y+4=0$  

$3+y+4=0$  

$7+y=0\mid -7$  

$y=-7$  

Zatem:

$\{\begin{array}{l}x=3\\ y=-7\end{array}$  

---

$\text{d)}$  

$\{\begin{array}{l}\frac{x-y}{2}+0,5=\frac{2x+y}{5}\mid \cdot 10\\ \frac{x-1}{2}=\frac{y+1}{4}\mid \cdot 4\end{array}$  

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

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

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

$\{\begin{array}{l}x-7y+5=0\mid -5\\ 2x-y=3\end{array}$  

$\{\begin{array}{l}x-7y=-5\mid \cdot \left(-2\right)\\ 2x-y=3\end{array}$  

$\{\begin{array}{l}-2x+14y=10\\ 2x-y=3\end{array}$   

 

Dodajemy do siebie lewe i prawe strony równań.

$+\{\begin{array}{l}-2x+14y=10\\ 2x-y=3\end{array}$   
_________________________

$13y=13\mid :13$  

$y=1$  

Wyznaczamy  $x$ .

$2x-y=3$  

$2x-1=3\mid +1$  

$2x=4\mid :2$  

$x=2$  

Zatem:

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