Solve for b
b=\frac{ia}{3}+\left(1-3i\right)
Solve for a
a=9+3i-3ib
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a-2+3ib+i=7+4i
Use the distributive property to multiply 3b+1 by i.
-2+3ib+i=7+4i-a
Subtract a from both sides.
3ib+i=7+4i-a+2
Add 2 to both sides.
3ib+i=-a+9+4i
Do the additions in 7+4i+2.
3ib=-a+9+4i-i
Subtract i from both sides.
3ib=-a+9+3i
Do the additions in 9+4i-i.
3ib=9+3i-a
The equation is in standard form.
\frac{3ib}{3i}=\frac{9+3i-a}{3i}
Divide both sides by 3i.
b=\frac{9+3i-a}{3i}
Dividing by 3i undoes the multiplication by 3i.
b=\frac{ia}{3}+\left(1-3i\right)
Divide -a+\left(9+3i\right) by 3i.
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