Solve y=y_{1}+(x-x_{1})i

$$y = y _ { 1 } + ( x - x _ { 1 } ) i$$

Solve for x

$$x=x_{1}-iy+iy_{1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-x_{1} by i.

$$y=y_{1}+ix-ix_{1}$$

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

$$y_{1}+ix-ix_{1}=y$$

Subtract y_{1} from both sides.

$$ix-ix_{1}=y-y_{1}$$

Subtract -ix_{1} from both sides.

$$ix=y-y_{1}-\left(-ix_{1}\right)$$

Multiply -1 and -i to get i.

$$ix=y-y_{1}+ix_{1}$$

The equation is in standard form.

$$ix=ix_{1}+y-y_{1}$$

Divide both sides by i.

$$\frac{ix}{i}=\frac{ix_{1}+y-y_{1}}{i}$$

Dividing by i undoes the multiplication by i.

$$x=\frac{ix_{1}+y-y_{1}}{i}$$

Divide y-y_{1}+ix_{1} by i.

$$x=x_{1}-iy+iy_{1}$$

Solve for x_1

$$x_{1}=x+iy-iy_{1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-x_{1} by i.

$$y=y_{1}+ix-ix_{1}$$

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

$$y_{1}+ix-ix_{1}=y$$

Subtract y_{1} from both sides.

$$ix-ix_{1}=y-y_{1}$$

Subtract ix from both sides.

$$-ix_{1}=y-y_{1}-ix$$

Reorder the terms.

$$-ix_{1}=-ix+y-y_{1}$$

Divide both sides by -i.

$$\frac{-ix_{1}}{-i}=\frac{-ix+y-y_{1}}{-i}$$

Dividing by -i undoes the multiplication by -i.

$$x_{1}=\frac{-ix+y-y_{1}}{-i}$$

Divide -ix+y-y_{1} by -i.

$$x_{1}=x+iy-iy_{1}$$