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Section 10.4 Solving a System of Equations in Multiple Variables
We can also solve a system of equations by placing the various equations in a list (by using curly brackets) inside the
solve() command.
\begin{equation*}
\displaystyle eq1\, := \,x-y=2
\end{equation*}
\begin{equation*}
\displaystyle eq2\, := \,y={x}^{2}-4
\end{equation*}
> solve( {eq1, eq2}, {x, y});
\begin{equation*}
\displaystyle \left\{ x=2,y=0 \right\} ,\, \left\{ x=-1,y=-3 \right\}
\end{equation*}
Example 10.2. Finding the Intersection of Two Functions (Continued).
Using a system of equations, we can complete the example from
Example 10.1 with either a single
solve() or
fsolve() command.
> solve( {y = x*ln(x), y = sin(x)}, {x,y} );
\begin{equation*}
\begin{array}{l}
\left\{ x=RootOf \left( \_Z\,\ln \left( \_Z \right) -\sin \left( \_Z \right) \right) ,\right.\\
\left. y=\sin \left( RootOf \left( \_Z\,\ln \left( \_Z \right)-\sin \left( \_Z \right) \right) \right) \right\}
\end{array}
\end{equation*}
Once again, we may find that fsolve() provides a more useful output.
> fsolve( {y = x*ln(x), y = sin(x)}, {x,y} );
\begin{equation*}
\displaystyle \left\{ x= 1.752677281,y= 0.9835052061 \right\}
\end{equation*}
