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Solve the system, if a is some real number:
$$
\begin{aligned}
&a x+y=1 \\
&x+a y=1
\end{aligned}
$$
ago in Mathematics by Diamond (78,880 points) | 4 views

1 Answer

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Best answer
\begin{aligned}
&a x+y=1 \\
&\frac{x+a y=1}{=} \\
&y=1-a x \\
&x+a(1-a x)=1 \\
&x+a-a^{2} x=1 \\
&x\left(1-a^{2}\right)=1-a \\
&x=\frac{1-a}{1-a^{2}}=\frac{1-a}{(1-a)(1+a)}=\frac{1}{a+1}
\end{aligned}
ago by Diamond (78,880 points)

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