Solve for y (complex solution)
\left\{\begin{matrix}\\y=\frac{5}{4}=1.25\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&\theta =0\end{matrix}\right.
Solve for θ (complex solution)
\left\{\begin{matrix}\\\theta =0\text{, }&\text{unconditionally}\\\theta \in \mathrm{C}\text{, }&y=\frac{5}{4}\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=\frac{5}{4}=1.25\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&\theta =0\end{matrix}\right.
Solve for θ
\left\{\begin{matrix}\\\theta =0\text{, }&\text{unconditionally}\\\theta \in \mathrm{R}\text{, }&y=\frac{5}{4}\end{matrix}\right.
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\frac{4}{5}y\theta =\theta
Swap sides so that all variable terms are on the left hand side.
\frac{4\theta }{5}y=\theta
The equation is in standard form.
\frac{5\times \frac{4\theta }{5}y}{4\theta }=\frac{5\theta }{4\theta }
Divide both sides by \frac{4}{5}\theta .
y=\frac{5\theta }{4\theta }
Dividing by \frac{4}{5}\theta undoes the multiplication by \frac{4}{5}\theta .
y=\frac{5}{4}
Divide \theta by \frac{4}{5}\theta .
\theta -\frac{4}{5}y\theta =0
Subtract \frac{4}{5}y\theta from both sides.
\left(1-\frac{4}{5}y\right)\theta =0
Combine all terms containing \theta .
\left(-\frac{4y}{5}+1\right)\theta =0
The equation is in standard form.
\theta =0
Divide 0 by 1-\frac{4}{5}y.
\frac{4}{5}y\theta =\theta
Swap sides so that all variable terms are on the left hand side.
\frac{4\theta }{5}y=\theta
The equation is in standard form.
\frac{5\times \frac{4\theta }{5}y}{4\theta }=\frac{5\theta }{4\theta }
Divide both sides by \frac{4}{5}\theta .
y=\frac{5\theta }{4\theta }
Dividing by \frac{4}{5}\theta undoes the multiplication by \frac{4}{5}\theta .
y=\frac{5}{4}
Divide \theta by \frac{4}{5}\theta .
\theta -\frac{4}{5}y\theta =0
Subtract \frac{4}{5}y\theta from both sides.
\left(1-\frac{4}{5}y\right)\theta =0
Combine all terms containing \theta .
\left(-\frac{4y}{5}+1\right)\theta =0
The equation is in standard form.
\theta =0
Divide 0 by 1-\frac{4}{5}y.
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