Property 8
If there are n distinct variables in a system of equations, n different equations which are independent (linearly independent) must be given for each variable to have a single solution.
1.
\(2xy-x+y-4=0\)
\(\Rightarrow x=?\)
2.
\(2x-y+xy-8=0\)
\(\Rightarrow y=?\)
3.
\(3ab-b+2a=0\)
\(\Rightarrow a=?\)
4.
\(4ab-2a+b=0\)
\(\Rightarrow b=?\)
5.
\(2xy-3x+4y-8=0\)
\(\Rightarrow y=?\)
6.
\(x+y=8\)
\(y+z=6\)
\(x+z=2\)
\(\Rightarrow x+y+z=?\)
7.
\(x+y=11\)
\(y+z=13\)
\(x+z=8\)
\(\Rightarrow x+y+z=?\)
8.
\(x,y,z\in\mathbb Z^+\)
\(x\cdot y=20\)
\(y\cdot z=35\)
\(x\cdot z=28\)
\(\Rightarrow z=?\)
9.
\(x,y,z\in\mathbb Z^-\)
\(x\cdot y=24\)
\(y\cdot z=18\)
\(x\cdot z=12\)
\(\Rightarrow y=?\)
10.
\(x+y=6\)
\(x\cdot z=2\)
\(y\cdot z=10\)
\(\Rightarrow z=?\)
11.
\(x+y=8\)
\(x\cdot z=13\)
\(y\cdot z=11\)
\(\Rightarrow z=?\)
12.
\(x-y=1\)
\(x\cdot z=8\)
\(y\cdot z=6\)
\(\Rightarrow z=?\)