solve(eqn1,...,eqnN) returns solutions to the system of equations with respect to variables found by findsym.

solve(eqn1,eqn2,...,eqnN, var1, var2,..., varN) returns solutions with respect to given variables.

If no closed-form solution is found and the number of equations is equal to number of variables, numeric solve is attempted.

Three different types of output are possible.  For one equation and one output, the resulting solution is returned with multiplicities for a polynomial equation in a vector.  For several variables and an equal number of outputs, the results are sorted and assigned to the outputs.  For several equations and a single output, a MTM[struct] containing the solutions is returned.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$t≔2+{\left(3+4\log \left(x\right)\right)}^2-5\log \left(x\right)\:$

$\mathrm{solve}\left(t\right)$

$\left[\begin{array}{c}{\ⅇ}^{-\frac{19}{32}+\frac{7\mathrm{I}\sqrt{7}}{32}}\\ {\ⅇ}^{-\frac{19}{32}-\frac{7\mathrm{I}\sqrt{7}}{32}}\end{array}\right]$

$\mathrm{solve}\left(p\sin \left(x\right)=r\right)$

$\arcsin \left(\frac{r}{p}\right)$

$x,y≔\mathrm{solve}\left(x^2+xy+y=3\,x^2-4x+3=0\right)$

$x,y≔\left[\begin{array}{c}1\\ 3\end{array}\right],\left[\begin{array}{c}1\\ -\frac{3}{2}\end{array}\right]$

$S≔\mathrm{solve}\left(u^2{v}^2-2u-1=0\,u^2-v^2-1=0\right)\:$

$S:-u$

$\left[\begin{array}{c}-\frac{1}{2}+\frac{\mathrm{I}\sqrt{3}}{2}\\ -\frac{1}{2}+\frac{\mathrm{I}\sqrt{3}}{2}\\ -\frac{1}{2}-\frac{\mathrm{I}\sqrt{3}}{2}\\ -\frac{1}{2}-\frac{\mathrm{I}\sqrt{3}}{2}\\ \frac{\sqrt{5}}{2}+\frac{1}{2}\\ \frac{\sqrt{5}}{2}+\frac{1}{2}\\ -\frac{\sqrt{5}}{2}+\frac{1}{2}\\ -\frac{\sqrt{5}}{2}+\frac{1}{2}\end{array}\right]$

$S:-v$

$\left[\begin{array}{c}\frac{\sqrt{-6-2\mathrm{I}\sqrt{3}}}{2}\\ -\frac{\sqrt{-6-2\mathrm{I}\sqrt{3}}}{2}\\ \frac{\sqrt{-6+2\mathrm{I}\sqrt{3}}}{2}\\ -\frac{\sqrt{-6+2\mathrm{I}\sqrt{3}}}{2}\\ \frac{\sqrt{2+2\sqrt{5}}}{2}\\ -\frac{\sqrt{2+2\sqrt{5}}}{2}\\ \frac{\sqrt{2-2\sqrt{5}}}{2}\\ -\frac{\sqrt{2-2\sqrt{5}}}{2}\end{array}\right]$

$S≔\mathrm{solve}\left(a{u}^2+v^2\,u-v=1\,a\,u\right)\:$

$S:-a$

$-\frac{v^2}{v^2+2v+1}$

$S:-u$

$v+1$

$a,u,v≔\mathrm{solve}\left(a{u}^2+v^2\,u-v=1\,a^2-5a+6\right)$

$a,u,v≔\left[\begin{array}{c}2\\ 2\\ 3\\ 3\end{array}\right],\left[\begin{array}{c}\frac{1}{3}+\frac{\mathrm{I}\sqrt{2}}{3}\\ \frac{1}{3}-\frac{\mathrm{I}\sqrt{2}}{3}\\ \frac{1}{4}+\frac{\mathrm{I}\sqrt{3}}{4}\\ \frac{1}{4}-\frac{\mathrm{I}\sqrt{3}}{4}\end{array}\right],\left[\begin{array}{c}-\frac{2}{3}+\frac{\mathrm{I}\sqrt{2}}{3}\\ -\frac{2}{3}-\frac{\mathrm{I}\sqrt{2}}{3}\\ -\frac{3}{4}+\frac{\mathrm{I}\sqrt{3}}{4}\\ -\frac{3}{4}-\frac{\mathrm{I}\sqrt{3}}{4}\end{array}\right]$