$a\text{)}\{\begin{array}{l}x-y=2\\ x=y^2-4\end{array}$  

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

$\{\begin{array}{l}{y}^2-y-6=0\\ x=y^2-4\end{array}$

Rozwiążmy równanie:  

$y^2-y-6=0$  

$\Delta ={\left(-1\right)}^2-4\cdot 1\cdot \left(-6\right)=1+24=5$  

$\sqrt{\Delta }=5$  

$y_1=\frac{1-5}{2}=\frac{-4}{2}=-2$  

$y_2=\frac{1+5}{2}=\frac{6}{2}=3$  

zatem:

$x_1={\left(-2\right)}^2-4=4-4=0$  

$x_2=3^2-4=9-4=5$  

więc:

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

lub

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

---

$b\text{)}\{\begin{array}{l}9x^2-4y^2=0\\ x-2y+4=0\end{array}$  

$\{\begin{array}{l}9x^2-4y^2=0\\ x=2y-4\end{array}$  

$\{\begin{array}{l}9\cdot {\left(2y-4\right)}^2-4y^2=0\\ x=2y-4\end{array}$

$\{\begin{array}{l}9\cdot \left(4y^2-16y+16\right)-4y^2=0\\ x=2y-4\end{array}$

$\{\begin{array}{l}36y^2-144y+144-4y^2=0\\ x=2y-4\end{array}$

$\{\begin{array}{l}32y^2-144y+144=0\\ x=2y-4\end{array}$

$\{\begin{array}{l}2y^2-9y+9=0\\ x=2y-4\end{array}$

Rozwiążmy równanie:

$2y^2-9y+9=0$  

$\Delta ={\left(-9\right)}^2-4\cdot 2\cdot 9=81-72=9$  

$\sqrt{\Delta }=3$  

$y_1=\frac{9-3}{4}=\frac{6}{4}=\frac{3}{2}$  

$y_2=\frac{9+3}{4}=\frac{12}{4}=3$  

zatem:

$x_1=2\cdot \frac{3}{2}-4=3-4=-1$  

$x_2=2\cdot 3-4=6-4=2$  

więc:

$\{\begin{array}{l}x=-1\\ y=\frac{3}{2}\end{array}$  

lub

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

---

$c\text{)}\{\begin{array}{l}x+{\left(y-2\right)}^2=6-4y\\ y=x\end{array}$  

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

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

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

Rozwiążmy równanie:

$y^2+y-2=0$  

$\Delta =1^2-4\cdot 1\cdot \left(-2\right)=1+8=9$  

$\sqrt{\Delta }=3$  

$y_1=\frac{-1-3}{2}=\frac{-4}{2}=-2$  

$y_2=\frac{-1+3}{2}=\frac{2}{2}=1$  

zatem:

$x_1=-2$  

$x_2=1$  

więc:

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

lub

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