Solve for x
x=\frac{11}{2}+\frac{3}{2}i-3iy
Solve for y
y=\frac{ix}{3}+\left(\frac{1}{2}-\frac{11}{6}i\right)
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11+3i=2x+6iy
Multiply 6 and i to get 6i.
2x+6iy=11+3i
Swap sides so that all variable terms are on the left hand side.
2x=11+3i-6iy
Subtract 6iy from both sides.
\frac{2x}{2}=\frac{11+3i-6iy}{2}
Divide both sides by 2.
x=\frac{11+3i-6iy}{2}
Dividing by 2 undoes the multiplication by 2.
x=\frac{11}{2}+\frac{3}{2}i-3iy
Divide 11+3i-6iy by 2.
11+3i=2x+6iy
Multiply 6 and i to get 6i.
2x+6iy=11+3i
Swap sides so that all variable terms are on the left hand side.
6iy=11+3i-2x
Subtract 2x from both sides.
\frac{6iy}{6i}=\frac{11+3i-2x}{6i}
Divide both sides by 6i.
y=\frac{11+3i-2x}{6i}
Dividing by 6i undoes the multiplication by 6i.
y=\frac{ix}{3}+\left(\frac{1}{2}-\frac{11}{6}i\right)
Divide 11+3i-2x by 6i.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}