Solve 4x-3+7i=5+2y-1

$$4x-3+7i = 5+2y-1$$

Solve for x

$$x=\frac{y}{2}+\left(\frac{7}{4}-\frac{7}{4}i\right)$$

Steps for Solving Linear Equation

Subtract 1 from 5 to get 4.

$$4x-3+7i=4+2y$$

Add 3 to both sides.

$$4x+7i=4+2y+3$$

Add 4 and 3 to get 7.

$$4x+7i=7+2y$$

Subtract 7i from both sides.

$$4x=7+2y-7i$$

The equation is in standard form.

$$4x=2y+\left(7-7i\right)$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{2y+\left(7-7i\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{2y+\left(7-7i\right)}{4}$$

Divide 7-7i+2y by 4.

$$x=\frac{y}{2}+\left(\frac{7}{4}-\frac{7}{4}i\right)$$

Solve for y

$$y=2x+\left(-\frac{7}{2}+\frac{7}{2}i\right)$$

Steps for Solving Linear Equation

Subtract 1 from 5 to get 4.

$$4x-3+7i=4+2y$$

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

$$4+2y=4x-3+7i$$

Subtract 4 from both sides.

$$2y=4x-3+7i-4$$

Do the additions in -3+7i-4.

$$2y=4x-7+7i$$

The equation is in standard form.

$$2y=4x+\left(-7+7i\right)$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{4x+\left(-7+7i\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{4x+\left(-7+7i\right)}{2}$$

Divide 4x+\left(-7+7i\right) by 2.

$$y=2x+\left(-\frac{7}{2}+\frac{7}{2}i\right)$$