Four Basic Operations In A System Of Equations

Algebra Level 3

\[\large {\begin{cases} { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 }+{ x }_{ 4 }=2015\\ { x }_{ 1 }-{ x }_{ 2 }-{ x }_{ 3 }-{ x }_{ 4 }=2\times 2015\\ { x }_{ 1 } \times { x }_{ 2 } \times { x }_{ 3 } \times { x }_{ 4 }=3\times 2015\\ { x }_{ 1 } \div { x }_{ 2 } \div { x }_{ 3 } \div { x }_{ 4 }=4\times 2015 \end{cases}}\]

Find the number of ordered quadruples \(({ x }_{ 1 },{ x }_{ 2 },{ x }_{ 3 },{ x }_{ 4 })\) of real numbers which satisfy the system of equations above.

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