Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{z_{3}}{y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{z_{3}}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.
Solve for y (complex solution)
\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{z_{3}}{x}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&z_{3}=0\text{ and }x=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{z_{3}}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z_{3}=0\text{ and }x=0\end{matrix}\right.
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xy^{2}=z_{3}y
Multiply y and y to get y^{2}.
y^{2}x=yz_{3}
The equation is in standard form.
\frac{y^{2}x}{y^{2}}=\frac{yz_{3}}{y^{2}}
Divide both sides by y^{2}.
x=\frac{yz_{3}}{y^{2}}
Dividing by y^{2} undoes the multiplication by y^{2}.
x=\frac{z_{3}}{y}
Divide z_{3}y by y^{2}.
xy^{2}=z_{3}y
Multiply y and y to get y^{2}.
y^{2}x=yz_{3}
The equation is in standard form.
\frac{y^{2}x}{y^{2}}=\frac{yz_{3}}{y^{2}}
Divide both sides by y^{2}.
x=\frac{yz_{3}}{y^{2}}
Dividing by y^{2} undoes the multiplication by y^{2}.
x=\frac{z_{3}}{y}
Divide z_{3}y by y^{2}.
Examples
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Matrix
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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
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