a)

$\{\begin{array}{l}\frac{x}{12}+\frac{y}{8}=1\mid \cdot 24\\ \frac{x-2}{4}-\frac{y-6}{2}=2\mid \cdot 4\end{array}$  

$\{\begin{array}{l}2x+3y=24\\ x-2-2\left(y-6\right)=8\end{array}$  

$\{\begin{array}{l}2x+3y=24\\ x-2-2y+12=8\mid -10\end{array}$      

$\{\begin{array}{l}2x+3y=24\\ x-2y=-2\mid \cdot \left(-2\right)\end{array}$  

$+\{\begin{array}{l}2x+3y=24\\ -2x+4y=4\end{array}$  

$2x-2x+3y+4y=24+4$  

$7y=28\mid :7$  

$y=4$  

Zatem otrzymujemy:

$\{\begin{array}{l}y=4\\ 2x+3\cdot 4=24\end{array}$  

$\{\begin{array}{l}y=4\\ 2x+12=24\mid -12\end{array}$  

$\{\begin{array}{l}y=4\\ 2x=12\mid :2\end{array}$  

$\{\begin{array}{l}y=4\\ x=6\end{array}$  

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b)

$\{\begin{array}{l}\frac{x}{5}-\frac{y}{2}=0\text{,}95\mid \cdot 100\\ \frac{2x-2}{5}+\frac{3-2y}{2}=3\mid \cdot 10\end{array}$  

$\{\begin{array}{l}20x-50y=95\mid :5\\ 2\left(2x-2\right)+5\left(3-2y\right)=30\end{array}$  

$\{\begin{array}{l}4x-10y=19\\ 4x-4+15-10y=30\mid -11\end{array}$  

$\{\begin{array}{l}4x-10y=19\\ 4x-10y=19\end{array}$  

Jest to układ nieoznaczony.

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c)

$\{\begin{array}{l}\frac{3x-1}{2}-\frac{4y-7}{3}=2\mid \cdot 6\\ \frac{3y-6}{4}-\frac{5-x}{6}=-1\frac{5}{12}\mid \cdot 12\end{array}$  

$\{\begin{array}{l}3\left(3x-1\right)-2\left(4y-7\right)=12\\ 3\left(3y-6\right)-2\left(5-x\right)=-17\end{array}$  

$\{\begin{array}{l}9x-3-8y+14=12\mid -11\\ 9y-18-10+2x=-17\mid +28\end{array}$  

$\{\begin{array}{l}9x-8y=1\mid \cdot 2\\ 2x+9y=11\mid \cdot \left(-9\right)\end{array}$  

$+\{\begin{array}{l}18x-16y=2\\ -18x-81y=-99\end{array}$  

$18x-18x-16y-81y=2-99$  

$-97y=-97\mid :\left(-97\right)$  

$y=1$  

Zatem otrzymujemy:

$\{\begin{array}{l}y=1\\ 2x+9\cdot 1=11\mid -9\end{array}$  

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

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

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d)

$\{\begin{array}{l}\frac{2x-y}{5}-\frac{y+2x}{4}=1\text{,}2\mid \cdot 20\\ \frac{2x+3y}{12}-\frac{4x-y}{8}=0\text{,}25\mid \cdot 24\end{array}$  

$\{\begin{array}{l}4\left(2x-y\right)-5\left(y+2x\right)=24\\ 2\left(2x+3y\right)-3\left(4x-y\right)=6\end{array}$  

$\{\begin{array}{l}8x-4y-5y-10x=24\\ 4x+6y-12x+3y=6\end{array}$  

$+\{\begin{array}{l}-2x-9y=24\\ -8x+9y=6\end{array}$  

$-2x-8x-9y+0y=24+6$  

$-10x=30\mid :\left(-10\right)$  

$x=-3$  

Zatem otrzymujemy:

$\{\begin{array}{l}x=-3\\ -2\cdot \left(-3\right)-9y=24\end{array}$  

$\{\begin{array}{l}x=-3\\ 6-9y=24\mid -6\end{array}$  

$\{\begin{array}{l}x=-3\\ -9y=18\mid :\left(-9\right)\end{array}$  

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