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[ammornil]

(a)
[tex]\begin{array}{|l} \frac{x+y}{9}-\frac{x-y}{3} =2 \\ \frac{3x-2y}{3}+23=2x \end{array} \Rightarrow \begin{array}{|l}x+y-3(x-y)=18 \\ 3x-2y+69=6x \end{array} \Rightarrow \begin{array}{|l}x+y-3x+3y=18 \\ 3x-2y+69-6x=0 \end{array} \Rightarrow[/tex]

[tex]\begin{array}{|l}-2x+4y=18 |:(-2) \\ -3x-2y+69=0 \end{array} \Rightarrow \begin{array}{|l}x-2y=-9 \\ -3x-2y=-69 \end{array} \Rightarrow \begin{array}{|l}x=2y-9 \\ -3(2y-9)-2y=-69 \end{array} \Rightarrow[/tex]

[tex]\begin{array}{|l}x=2y-9 \\ -6y+27-2y=-69 \end{array} \Rightarrow \begin{array}{|l}x=2y-9 \\ -8y=-69-27 \end{array} \Rightarrow \begin{array}{|l}x=2.12-9 \\ y=12 \end{array} \Rightarrow \begin{array}{|l}x=15 \\ y=12 \end{array} \Rightarrow[/tex]

[ammornil]

(б)
[tex]\begin{array}{|l} y(x-2)=(1+y)(x-3) \\ x(x+1)-1=x(x-2)-y \end{array} \Rightarrow \begin{array}{|l}\cancel{xy}-2y=x-3\cancel{+xy}-3y \\ \cancel{x^{2}}+x-1=\cancel{x^{2}}-2x-y \end{array} \Rightarrow \begin{array}{|l} -2y+3y=x-3 \\ x+2x=1-y \end{array} \Rightarrow[/tex]

[tex]\begin{array}{|l} 1-3x=x-3 \\ y=1-3x \end{array} \Rightarrow \begin{array}{|l}-4x=-4 \\ y=1-3x \end{array} \Rightarrow \begin{array}{|l}x=1 \\ y=1-3.1 \end{array} \Rightarrow \begin{array}{|l}x=1 \\ y=-2 \end{array} \Rightarrow[/tex]