Đáp án:
\(a = \pm 2\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
{a^2}x - y = - 7\\
2x + y = 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {{a^2} + 2} \right)x = - 6\\
y = 1 - 2x
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{ - 6}}{{{a^2} + 2}}\\
y = 1 - 2.\left( {\dfrac{{ - 6}}{{{a^2} + 2}}} \right)
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{ - 6}}{{{a^2} + 2}}\\
y = \dfrac{{{a^2} + 2 + 12}}{{{a^2} + 2}} = \dfrac{{{a^2} + 14}}{{{a^2} + 2}}
\end{array} \right.\\
Do:x + y = 2\\
\to \dfrac{{ - 6}}{{{a^2} + 2}} + \dfrac{{{a^2} + 14}}{{{a^2} + 2}} = 2\\
\to {a^2} + 8 = 2{a^2} + 4\\
\to {a^2} = 4\\
\to a = \pm 2
\end{array}\)
