Solve 8+(3x+y)i=2x-4i

$$8 + ( 3 x + y ) i = 2 x - 4 i$$

Solve for x

$$x=\left(-\frac{3}{13}+\frac{2}{13}i\right)y+\left(\frac{4}{13}+\frac{32}{13}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x+y by i.

$$8+3ix+iy=2x-4i$$

Subtract 2x from both sides.

$$8+3ix+iy-2x=-4i$$

Combine 3ix and -2x to get \left(-2+3i\right)x.

$$8+\left(-2+3i\right)x+iy=-4i$$

Subtract 8 from both sides.

$$\left(-2+3i\right)x+iy=-4i-8$$

Subtract iy from both sides.

$$\left(-2+3i\right)x=-4i-8-iy$$

Reorder the terms.

$$\left(-2+3i\right)x=-iy-8-4i$$

The equation is in standard form.

$$\left(-2+3i\right)x=-8-4i-iy$$

Divide both sides by -2+3i.

$$\frac{\left(-2+3i\right)x}{-2+3i}=\frac{-8-4i-iy}{-2+3i}$$

Dividing by -2+3i undoes the multiplication by -2+3i.

$$x=\frac{-8-4i-iy}{-2+3i}$$

Divide -iy+\left(-8-4i\right) by -2+3i.

$$x=\left(-\frac{3}{13}+\frac{2}{13}i\right)y+\left(\frac{4}{13}+\frac{32}{13}i\right)$$

Solve for y

$$y=\left(-3-2i\right)x+\left(-4+8i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x+y by i.

$$8+3ix+iy=2x-4i$$

Subtract 8 from both sides.

$$3ix+iy=2x-4i-8$$

Subtract 3ix from both sides.

$$iy=2x-4i-8-3ix$$

Combine 2x and -3ix to get \left(2-3i\right)x.

$$iy=\left(2-3i\right)x-4i-8$$

The equation is in standard form.

$$iy=\left(2-3i\right)x+\left(-8-4i\right)$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{\left(2-3i\right)x+\left(-8-4i\right)}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{\left(2-3i\right)x+\left(-8-4i\right)}{i}$$

Divide \left(2-3i\right)x+\left(-8-4i\right) by i.

$$y=\left(-3-2i\right)x+\left(-4+8i\right)$$