Solve x-3i=(8x-y)i

$$x - 3 i = ( 8 x - y ) i$$

Solve for x

$$x=\left(\frac{8}{65}-\frac{1}{65}i\right)y+\left(-\frac{24}{65}+\frac{3}{65}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8x-y by i.

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

Subtract 8ix from both sides.

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

Combine x and -8ix to get \left(1-8i\right)x.

$$\left(1-8i\right)x-3i=-iy$$

Add 3i to both sides.

$$\left(1-8i\right)x=-iy+3i$$

The equation is in standard form.

$$\left(1-8i\right)x=3i-iy$$

Divide both sides by 1-8i.

$$\frac{\left(1-8i\right)x}{1-8i}=\frac{3i-iy}{1-8i}$$

Dividing by 1-8i undoes the multiplication by 1-8i.

$$x=\frac{3i-iy}{1-8i}$$

Divide -iy+3i by 1-8i.

$$x=\left(\frac{8}{65}-\frac{1}{65}i\right)y+\left(-\frac{24}{65}+\frac{3}{65}i\right)$$

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply 8x-y by i.

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

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

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

Subtract 8ix from both sides.

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

Combine x and -8ix to get \left(1-8i\right)x.

$$-iy=\left(1-8i\right)x-3i$$

Divide both sides by -i.

$$\frac{-iy}{-i}=\frac{\left(1-8i\right)x-3i}{-i}$$

Dividing by -i undoes the multiplication by -i.

$$y=\frac{\left(1-8i\right)x-3i}{-i}$$

Divide \left(1-8i\right)x-3i by -i.

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