$a)$  

$\{\begin{array}{l}{\left(x+3\right)}^2-{\left(y-1\right)}^2=\left(x-y\right)\left(x+y\right)\\ 3x-7y=0\end{array}$  

Korzystamy z wzorów skróconego mnożenia:

$\{\begin{array}{l}{x}^2+2\cdot x\cdot 3+3^2-\left(y^2-2\cdot y\cdot 1+1^2\right)=x^2-y^2\\ 3x-7y=0\mid +7y\end{array}$  

$\{\begin{array}{l}{x}^2+6x+9-\left(y^2-2y+1\right)=x^2-y^2\\ 3x=7y\mid :3\end{array}$  

$\{\begin{array}{l}{x}^2+6x+\underline{9}-y^2+2y-\underline{1}=x^2-y^2\mid -x^2+y^2\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}6x+2y+8=0\mid -8\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}6x+2y=-8\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}6\cdot \frac{7}{3}y+2y=-8\\ x=\frac{7}{3}y\end{array}$ $\{\begin{array}{l}6\cdot \frac{7}{3}y+2y=-8\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}\frac{42}{3}y+\frac{6}{3}y=-8\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}\frac{48}{3}y=-8\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}16y=-8\mid :16\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}y=-\frac{8}{16}\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}y=-\frac{1}{2}\\ x=\frac{7}{3}y\end{array}$  

$\{\begin{array}{l}y=-\frac{1}{2}\\ x=\frac{7}{3}\cdot \left(-\frac{1}{2}\right)\end{array}$  

$\{\begin{array}{l}y=-\frac{1}{2}\\ x=-\frac{7}{6}\end{array}$  

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

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

 

$b)$  

$\{\begin{array}{l}{\left(x-5\right)}^2-{\left(x+2\right)}^2=7y\\ {\left(y+4\right)}^2-\left(y-2\right)\left(y+2\right)=8x\end{array}$  

Korzystamy z wzorów skróconego mnożenia:

$\{\begin{array}{l}{x}^2-2\cdot x\cdot 5+5^2-\left(x^2+2\cdot x\cdot 2+2^2\right)=7y\\ y^2+2\cdot y\cdot 4+4^2-\left(y^2-2^2\right)=8x\end{array}$  

$\{\begin{array}{l}\sout{x^2}-\underline{10x}+\underline{\underline{25}}-\sout{x^2}-\underline{4x}-\underline{\underline{4}}=7y\\ \sout{y^2}+8y+\underline{16}-\sout{y^2}+\underline{4}=8x\end{array}$  

$\{\begin{array}{l}-14x+21=7y\mid :7\\ 8y+20=8x\mid :4\end{array}$  

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

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

$\{\begin{array}{l}y=-2x+3\\ -4x+6+5=2x\end{array}$  

$\{\begin{array}{l}y=-2x+3\\ -4x+11=2x\mid -2x-11\end{array}$  

$\{\begin{array}{l}y=-2x+3\\ -6x=-11\mid :\left(-6\right)\end{array}$  

$\{\begin{array}{l}y=-2x+3\\ x=\frac{-11}{-6}\end{array}$  

$\{\begin{array}{l}y=-2x+3\\ x=\frac{11}{6}\end{array}$  

$\{\begin{array}{l}x=\frac{11}{6}\\ y=-2\cdot \frac{11}{6}+3\end{array}$  

$\{\begin{array}{l}x=\frac{11}{6}\\ y=-\frac{11}{3}+3\end{array}$  

$\{\begin{array}{l}x=\frac{11}{6}\\ y=-\frac{11}{3}+\frac{9}{3}\end{array}$  

$\{\begin{array}{l}x=\frac{11}{6}\\ y=-\frac{2}{3}\end{array}$  

$\{\begin{array}{l}x=1\frac{5}{6}\\ y=-\frac{2}{3}\end{array}$