$\text{a)}$  

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

Podstawiamy x=2 do pierwszego równania.

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

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

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

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

---

$\text{b)}$  

$\{\begin{array}{l}2x-y=7\\ y=-3\end{array}$  

Podstawiamy y=-3 do pierwszego równania.

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

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

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

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

---

$\text{c)}$  

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

Podstawiamy x=2y do pierwszego równania.

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

$\{\begin{array}{l}8y-7y=2\\ x=2y\end{array}$  

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

Podstawiamy y=2 do drugiego równania.

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

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

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

---

$\text{d)}$  

$\{\begin{array}{l}3x+4y=15\\ y=-2x\end{array}$  

Podstawiamy y=-2x do pierwszego równania.

$\{\begin{array}{l}3x+4\cdot \left(-2x\right)=15\\ y=-2x\end{array}$  

$\{\begin{array}{l}3x-8x=15\\ y=-2x\end{array}$  

$\{\begin{array}{l}-5x=15\mid :\left(-5\right)\\ y=-2x\end{array}$  

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

Podstawiamy x=-3 do drugiego równania.

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

$\{\begin{array}{l}x=-3\\ y=6\end{array}$  

---

$\text{e)}$  

$\{\begin{array}{l}3x-y=3\\ 2x+3y=13\end{array}$  

$\{\begin{array}{l}y=3x-3\\ 2x+3y=13\end{array}$  

Podstawiamy y=3x-3 do drugiego równania.

$\{\begin{array}{l}y=3x-3\\ 2x+3\left(3x-3\right)=13\end{array}$  

$\{\begin{array}{l}y=3x-3\\ 2x+9x-9=13\end{array}$  

$\{\begin{array}{l}y=3x-3\\ 11x=22\mid :11\end{array}$  

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

Podstawiamy x=2 do pierwszego równania.

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

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

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

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

---

$\text{f)}$  

$\{\begin{array}{l}3x+4y=-2\\ -2x+6y=10\mid :\left(-2\right)\end{array}$  

$\{\begin{array}{l}3x+4y=-2\\ x-3y=-5\end{array}$  

$\{\begin{array}{l}3x+4y=-2\\ x=3y-5\end{array}$  

Podstawiamy x=3y-5 do pierwszego równania.

$\{\begin{array}{l}3\left(3y-5\right)+4y=-2\\ x=3y-5\end{array}$  

$\{\begin{array}{l}9y-15+4y=-2\\ x=3y-5\end{array}$  

$\{\begin{array}{l}13y=13\mid :13\\ x=3y-5\end{array}$  

$\{\begin{array}{l}y=1\\ x=3y-5\end{array}$  

Podstawiamy y=1 do drugiego równania.

$\{\begin{array}{l}y=1\\ x=3\cdot 1-5\end{array}$  

$\{\begin{array}{l}y=1\\ x=3-5\end{array}$  

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

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