Solve for x
x=\left(-\frac{3}{13}-\frac{11}{13}i\right)y+\left(\frac{17}{13}-\frac{33}{13}i\right)
Solve for y
y=\left(-\frac{3}{10}+\frac{11}{10}i\right)x+\left(-\frac{12}{5}-\frac{11}{5}i\right)
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3x-y+2ix+3iy=9-5i
Use the distributive property to multiply 2x+3y by i.
\left(3+2i\right)x-y+3iy=9-5i
Combine 3x and 2ix to get \left(3+2i\right)x.
\left(3+2i\right)x+\left(-1+3i\right)y=9-5i
Combine -y and 3iy to get \left(-1+3i\right)y.
\left(3+2i\right)x=9-5i-\left(-1+3i\right)y
Subtract \left(-1+3i\right)y from both sides.
\left(3+2i\right)x=9-5i+\left(1-3i\right)y
Multiply -1 and -1+3i to get 1-3i.
\left(3+2i\right)x=\left(1-3i\right)y+\left(9-5i\right)
The equation is in standard form.
\frac{\left(3+2i\right)x}{3+2i}=\frac{\left(1-3i\right)y+\left(9-5i\right)}{3+2i}
Divide both sides by 3+2i.
x=\frac{\left(1-3i\right)y+\left(9-5i\right)}{3+2i}
Dividing by 3+2i undoes the multiplication by 3+2i.
x=\left(-\frac{3}{13}-\frac{11}{13}i\right)y+\left(\frac{17}{13}-\frac{33}{13}i\right)
Divide 9-5i+\left(1-3i\right)y by 3+2i.
3x-y+2ix+3iy=9-5i
Use the distributive property to multiply 2x+3y by i.
\left(3+2i\right)x-y+3iy=9-5i
Combine 3x and 2ix to get \left(3+2i\right)x.
\left(3+2i\right)x+\left(-1+3i\right)y=9-5i
Combine -y and 3iy to get \left(-1+3i\right)y.
\left(-1+3i\right)y=9-5i-\left(3+2i\right)x
Subtract \left(3+2i\right)x from both sides.
\left(-1+3i\right)y=9-5i+\left(-3-2i\right)x
Multiply -1 and 3+2i to get -3-2i.
\left(-1+3i\right)y=\left(-3-2i\right)x+\left(9-5i\right)
The equation is in standard form.
\frac{\left(-1+3i\right)y}{-1+3i}=\frac{\left(-3-2i\right)x+\left(9-5i\right)}{-1+3i}
Divide both sides by -1+3i.
y=\frac{\left(-3-2i\right)x+\left(9-5i\right)}{-1+3i}
Dividing by -1+3i undoes the multiplication by -1+3i.
y=\left(-\frac{3}{10}+\frac{11}{10}i\right)x+\left(-\frac{12}{5}-\frac{11}{5}i\right)
Divide 9-5i+\left(-3-2i\right)x by -1+3i.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}