a)

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

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

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

$\{\begin{array}{l}7-y=14-4y-4y\\ x=7-2y\end{array}$  

$\{\begin{array}{l}7-y=14-8y\mid +8y-7\\ x=7-2y\end{array}$  

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

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

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

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

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b)

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

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

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

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

$\{\begin{array}{l}3x=1\mid :3\\ y=2+x\end{array}$  

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

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

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c)

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

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

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

$\{\begin{array}{l}2\left(2y-13\right)=y-2\\ x=2y-15\end{array}$  

$\{\begin{array}{l}4y-26=y-2\mid -y+26\\ x=2y-15\end{array}$  

$\{\begin{array}{l}3y=24\mid :3\\ x=2y-15\end{array}$  

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

$\{\begin{array}{l}y=8\\ x=16-15\end{array}$  

$\{\begin{array}{l}y=8\\ x=1\end{array}$