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[tex]\begin{gathered} \text{ We will verify which of the given points satisfy the thr}e\text{ equations:} \\ 3x-y-z=8 \\ 2x+y+z=3 \\ x-y+z=3 \end{gathered}[/tex][tex]\begin{gathered} \text{ We will verify for (3,3,-2)} \\ 3(3)-3-(-2)=9-3+2=8 \\ 2(3)+3-2=6+3-2=7\ne3,\text{ so (3,3,-2) is not the solution} \end{gathered}[/tex][tex]\begin{gathered} \text{ now, for (-3,-4,-13)} \\ 3(-3)-(-4)-(-13)=-9+4+13=8 \\ 2(-3)+(-4)+(-13)=-6-4-13=-23\text{ }\ne3,\text{ } \\ \text{thus (-3,-4,-13) is not the solution} \end{gathered}[/tex][tex]\begin{gathered} \text{ for (2,-1.5,-0.5)} \\ 3(2)-(-1.5)-(-0.5)=6+1.5+0.5=8 \\ 2(2)+(-1.5)+(-0.5)=4-1.5-0.5=2\ne3 \\ \text{ So (2,-1.5,-0.5) is not the solution} \end{gathered}[/tex][tex]\begin{gathered} \text{ The solution must be then (3,-1,2), let's verify it} \\ 3(3)+1-2=9+1-2=8 \\ 2(3)-1-2=6-1-2=3 \\ (3)+1+2=6 \\ \\ \text{ Indeed, the solution is (3,-1,2)} \end{gathered}[/tex]
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