Solve for A
\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&D=\frac{BI}{5}\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{5D}{I}\text{, }&I\neq 0\\B\in \mathrm{R}\text{, }&A=0\text{ or }\left(D=0\text{ and }I=0\right)\end{matrix}\right.
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IAB=5AD
Multiply both sides of the equation by 5.
IAB-5AD=0
Subtract 5AD from both sides.
\left(IB-5D\right)A=0
Combine all terms containing A.
\left(BI-5D\right)A=0
The equation is in standard form.
A=0
Divide 0 by IB-5D.
IAB=5AD
Multiply both sides of the equation by 5.
AIB=5AD
The equation is in standard form.
\frac{AIB}{AI}=\frac{5AD}{AI}
Divide both sides by IA.
B=\frac{5AD}{AI}
Dividing by IA undoes the multiplication by IA.
B=\frac{5D}{I}
Divide 5AD by IA.
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