$\text{a)}\{\begin{array}{l}x+2y=\frac{1}{2}\mid -2y\\ 5x+3y=\frac{3}{4}\end{array}$  

$\{\begin{array}{l}x=\frac{1}{2}-2y\\ 5\left(\frac{1}{2}-2y\right)+3y=\frac{3}{4}\end{array}$  

$\{\begin{array}{l}x=\frac{1}{2}-2y\\ \frac{5}{2}-10y+3y=\frac{3}{4}\mid -\frac{5}{2}\end{array}$  

$\{\begin{array}{l}x=\frac{1}{2}-2y\\ -7y=\frac{3}{4}-\frac{10}{4}\end{array}$  

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

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

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

$\{\begin{array}{l}x=0\\ y=\frac{1}{4}\end{array}$ $\{\begin{array}{l}x=0\\ y=\frac{1}{4}\end{array}$  

$\underline{\underline{}}$  

$\text{b)}\{\begin{array}{l}4x-y=\frac{1}{5}\\ \frac{1}{5}x+y=4\mid -\frac{1}{5}x\end{array}$  

$\{\begin{array}{l}4x-y=\frac{1}{5}\\ y=4-\frac{1}{5}x\end{array}$  

$\{\begin{array}{l}4x-\left(4-\frac{1}{5}x\right)=\frac{1}{5}\\ y=4-\frac{1}{5}x\end{array}$  

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

$\{\begin{array}{l}4\frac{1}{5}x=4\frac{1}{5}\\ y=4-\frac{1}{5}x\end{array}$  

$\{\begin{array}{l}x=1\\ y=4-\frac{1}{5}\cdot 1\end{array}$  

$\{\begin{array}{l}x=1\\ y=3\frac{4}{5}\end{array}$  

$\underline{\underline{}}$  

$\text{c)}\{\begin{array}{l}2x-3y=0,7\\ x+4y=5,3\mid -4y\end{array}$  

$\{\begin{array}{l}2x-3y=0,7\\ x=5,3-4y\end{array}$  

$\{\begin{array}{l}2\left(5,3-4y\right)-3y=0,7\\ x=5,3-4y\end{array}$  

$\{\begin{array}{l}10,6-8y-3y=0,7\mid -10,6\\ x=5,3-4y\end{array}$  

$\{\begin{array}{l}-11y=-9,9\mid :\left(-11\right)\\ x=5,3-4y\end{array}$  

$\{\begin{array}{l}y=0,9\\ x=5,3-4\cdot 0,9\end{array}$  

$\{\begin{array}{l}y=0,9\\ x=5,3-3,6\end{array}$  

$\{\begin{array}{l}y=0,9\\ x=1,7\end{array}$  

$\underline{\underline{}}$  

$\text{d)}\{\begin{array}{l}0,4x-0,3y=-2\mid \cdot 10\\ 2,1x+3,2y=85\mid \cdot 10\end{array}$   

Mnożymy oba równania przez 10, aby otzrymać zamiast ułamków dziesiętnych liczby całkowite.

$\{\begin{array}{l}4x-3y=-20\mid +3y\\ 21x+32y=850\end{array}$

$\{\begin{array}{l}4x=-20+3y\mid :4\\ 21x+32y=850\end{array}$  

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ 21\left(-5+\frac{3}{4}y\right)+32y=850\end{array}$  

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ -105+\frac{63}{4}y+32y=850\mid +105\end{array}$  

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ \frac{63}{4}y+\frac{128}{4}y=955\end{array}$   

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ \frac{191}{4}y=955\mid \cdot \frac{4}{191}\end{array}$

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ y={\sout{955}}^5\cdot \frac{4}{{\sout{191}}^1}\end{array}$   

$\{\begin{array}{l}x=-5+\frac{3}{4}y\\ y=20\end{array}$  

$\{\begin{array}{l}x=-5+\frac{3}{{\sout{4}}^1}\cdot {\sout{20}}^5\\ y=20\end{array}$   

$\{\begin{array}{l}x=10\\ y=20\end{array}$