Đáp án: A
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
2x + y = 1\\
{x^2} - 5xy + {y^2} = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1 - 2x\\
{x^2} - 5x\left( {1 - 2x} \right) + {\left( {1 - 2x} \right)^2} = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1 - 2x\\
{x^2} - 5x + 10{x^2} + 4{x^2} - 4x + 1 = 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1 - 2x\\
15{x^2} - 9x - 6 = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1 - 2x\\
15{x^2} - 15x + 6x - 6 = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
y = 1 - 2x\\
\left( {x - 1} \right)\left( {15x + 6} \right) = 0
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1;y = - 1\\
x = - \frac{6}{{15}} = - \frac{2}{5};y = \frac{9}{5}
\end{array} \right.\\
\Rightarrow 5\left( {{y_1} + {y_2}} \right) = 5\left( { - 1 + \frac{9}{5}} \right) = 4
\end{array}$
