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$\displaystyle\left \{{{3*(x-2)-2*(y+1)=-16} \atop {5*(x-3)+8*(y-2)=51}} \right. \Rightarrow\left \{{{3x-6-2y-2=-16} \atop {5x-15+8y-16=51}} \right. \Rightarrow\\\\\\ \Rightarrow \left \{{{3x-2y=-8}*4\atop {5x+8y=82}} \right. \Rightarrow \left \{{{12x-8y=-32} \atop {5x+8y=82}} \right. \Rightarrow \left \{{{17x=50} \atop {5x+8y=82}} \right. \Rightarrow$

$\displaystyle\Rightarrow \left \{{{x=\frac{50}{17}} \atop {\frac{5*50}{17} +8y=82}} \right. \Rightarrow \left \{{{x=\frac{50}{17}} \atop {8y=82-\frac{250}{17}}} \right. \Rightarrow\left \{{{x=\frac{50}{17} } \atop 8y=\frac{1144}{17}}} \right. \Rightarrow \left \{{{x=\frac{50}{17}} \atop {y=\frac{143}{17}}} \right.$

3x - 6 -2y -2=-16,

5x-15 + 8y -16=51

3x-2y=-8 (*4)

5x+8y=82

12x-8y=-32

5x+8y=82

17x=50;

x=50/17

5((50/17)-3)+8(y-2)=51

5(2+16/17 -3)+8y=67

5(-1 + 16/17)-67=-8y

-5+80/17 - 67 =-8y;

-72+80/17 = -8y

y=(-72+80/17)/(-8)

y=143/17