Solve -2x-i=1+3yi

$$- 2 x - i = 1 + 3 y i$$

Solve for x

$$x=-\frac{3iy}{2}+\left(-\frac{1}{2}-\frac{1}{2}i\right)$$

Steps for Solving Linear Equation

Multiply 3 and i to get 3i.

$$-2x-i=1+3iy$$

Add i to both sides.

$$-2x=1+3iy+i$$

The equation is in standard form.

$$-2x=3iy+\left(1+i\right)$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{3iy+\left(1+i\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{3iy+\left(1+i\right)}{-2}$$

Divide 1+i+3iy by -2.

$$x=-\frac{3iy}{2}+\left(-\frac{1}{2}-\frac{1}{2}i\right)$$

Solve for y

$$y=\frac{2ix}{3}+\left(-\frac{1}{3}+\frac{1}{3}i\right)$$

Steps for Solving Linear Equation

Multiply 3 and i to get 3i.

$$-2x-i=1+3iy$$

Swap sides so that all variable terms are on the left hand side.

$$1+3iy=-2x-i$$

Subtract 1 from both sides.

$$3iy=-2x-i-1$$

The equation is in standard form.

$$3iy=-1-i-2x$$

Divide both sides by 3i.

$$\frac{3iy}{3i}=\frac{-1-i-2x}{3i}$$

Dividing by 3i undoes the multiplication by 3i.

$$y=\frac{-1-i-2x}{3i}$$

Divide -2x+\left(-1-i\right) by 3i.

$$y=\frac{2ix}{3}+\left(-\frac{1}{3}+\frac{1}{3}i\right)$$