query: Solve in $\mathbb{R^{3}}$ : $\begin{cases}x+y+xy=19\\y+z+yz=11\\x+z+xz=14\end{cases}$
positive_passages.docid: 135742
positive_passages.text: Solve system of simultaneous equations in $3$ variables: $x+y+xy=19$, $y+z+yz=11$, $z+x+zx=14$
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 73538
negative_passages.text: solving $\cos z + \sin z = i$
negative_passages.docid: 40063
negative_passages.text: $x^2+y^2=z^n$: Find solutions without Pythagoras!
negative_passages.docid: 68960
negative_passages.text: How to solve $ 13x \equiv 1 ~ (\text{mod} ~ 17) $?
negative_passages.docid: 50283
negative_passages.text: Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$
negative_passages.docid: 18313
negative_passages.text: show this inequality with $xy+yz+zx=3$
negative_passages.docid: 149254
negative_passages.text: Solving $y^3=x^3+8x^2-6x+8$
negative_passages.docid: 115101
negative_passages.text: Solve $x + \lfloor y \rfloor + \{ z \} = 13.2$; $\{ x \} + y + \lfloor z \rfloor = 15.1$; $\lfloor x \rfloor + \{ y \} + z = 14.3$
negative_passages.docid: 44744
negative_passages.text: Integer solutions of $xy+9(x+y)=2006$
negative_passages.docid: 62980
negative_passages.text: How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$?
negative_passages.docid: 28274
negative_passages.text: Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
negative_passages.docid: 80982
negative_passages.text: Solve $a^3+b^3+3ab=1$ with $(a,b)\in \Bbb{Z}^2$
negative_passages.docid: 102860
negative_passages.text: solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$
negative_passages.docid: 131395
negative_passages.text: Solving linear congruence $2x + 11 \equiv 7 \pmod 3$
negative_passages.docid: 102320
negative_passages.text: Is my solution correct for solving $\cos(z)=2$, $z\in \mathbb{C}$
negative_passages.docid: 92692
negative_passages.text: Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$