Question

Given the system of equations, what is the value of the system determinant? 2x + y = 8 x - y = 10 -1 -2 -3

Answer 1

The real answer is -1

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Answer 2

`\left\{\begin{array}{ccc}ax+by=c\\dx+ye=f\end{array}\right\\\\\\D=\left|\begin{array}{ccc}a&b\\d&e\end{array}\right|=ae-db\\\\D_x=\left|\begin{array}{ccc}c&b\\f&e\end{array}\right|=ec-fb\\\\D_y=\left|\begin{array}{ccc}a&c\\d&f\end{array}\right|=fa-cd\\\\x=(D_x)/(D),\ y=(D_y)/(D)\\--------------------`

`\left\{\begin{array}{ccc}2x+y=8\\x-y=10\end{array}\right\\\\D=\left|\begin{array}{ccc}2&1\\1&-1\end{array}\right|=(2)(-1)-(1)(1)=-2-1=-3\\\\D_x=\left|\begin{array}{ccc}8&1\\10&-1\end{array}\right|=(8)(-1)-(10)(1)=-8-10=-18\\\\D_y=\left|\begin{array}{ccc}2&8\\1&10\end{array}\right|=(2)(10)-(1)(8)=20-8=12\\\\x=(-18)/(-3)=6\\\\y=(12)/(-3)=-4`