Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{5}{ey}\text{, }&y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y\neq 0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=\frac{5}{ea}\text{ and }a\neq 0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{5}{ey}\text{, }&y\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=\frac{5}{ea}\text{ and }a\neq 0\end{matrix}\right.
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5x=axey
Multiply both sides of the equation by y.
axey=5x
Swap sides so that all variable terms are on the left hand side.
exya=5x
The equation is in standard form.
\frac{exya}{exy}=\frac{5x}{exy}
Divide both sides by xey.
a=\frac{5x}{exy}
Dividing by xey undoes the multiplication by xey.
a=\frac{5}{ey}
Divide 5x by xey.
5x=axey
Multiply both sides of the equation by y.
5x-axey=0
Subtract axey from both sides.
-eaxy+5x=0
Reorder the terms.
\left(-eay+5\right)x=0
Combine all terms containing x.
\left(5-eay\right)x=0
The equation is in standard form.
x=0
Divide 0 by 5-yae.
5x=axey
Multiply both sides of the equation by y.
axey=5x
Swap sides so that all variable terms are on the left hand side.
exya=5x
The equation is in standard form.
\frac{exya}{exy}=\frac{5x}{exy}
Divide both sides by xey.
a=\frac{5x}{exy}
Dividing by xey undoes the multiplication by xey.
a=\frac{5}{ey}
Divide 5x by xey.
5x=axey
Multiply both sides of the equation by y.
5x-axey=0
Subtract axey from both sides.
-eaxy+5x=0
Reorder the terms.
\left(-eay+5\right)x=0
Combine all terms containing x.
\left(5-eay\right)x=0
The equation is in standard form.
x=0
Divide 0 by 5-yae.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}