Solve for x_3 (complex solution)
\left\{\begin{matrix}x_{3}=\frac{3x}{y}+2\text{, }&y\neq 0\\x_{3}\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
Solve for x
x=\frac{y\left(x_{3}-2\right)}{3}
Solve for x_3
\left\{\begin{matrix}x_{3}=\frac{3x}{y}+2\text{, }&y\neq 0\\x_{3}\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.
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1x_{3}y=3x+2y
Swap sides so that all variable terms are on the left hand side.
x_{3}y=3x+2y
Reorder the terms.
yx_{3}=3x+2y
The equation is in standard form.
\frac{yx_{3}}{y}=\frac{3x+2y}{y}
Divide both sides by y.
x_{3}=\frac{3x+2y}{y}
Dividing by y undoes the multiplication by y.
x_{3}=\frac{3x}{y}+2
Divide 3x+2y by y.
3x=1x_{3}y-2y
Subtract 2y from both sides.
3x=x_{3}y-2y
Reorder the terms.
\frac{3x}{3}=\frac{y\left(x_{3}-2\right)}{3}
Divide both sides by 3.
x=\frac{y\left(x_{3}-2\right)}{3}
Dividing by 3 undoes the multiplication by 3.
1x_{3}y=3x+2y
Swap sides so that all variable terms are on the left hand side.
x_{3}y=3x+2y
Reorder the terms.
yx_{3}=3x+2y
The equation is in standard form.
\frac{yx_{3}}{y}=\frac{3x+2y}{y}
Divide both sides by y.
x_{3}=\frac{3x+2y}{y}
Dividing by y undoes the multiplication by y.
x_{3}=\frac{3x}{y}+2
Divide 3x+2y by y.
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Limits
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