Solve 2+3i+2y=x+1+3i

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

Solve for x

$$x=2y+1$$

Solution Steps

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

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

Subtract 1 from both sides.

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

Do the additions in 2+3i-1.

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

Subtract 3i from both sides.

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

Do the additions in 1+3i-3i.

$$x=2y+1$$

Solve for y

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

Steps for Solving Linear Equation

Subtract 2+3i from both sides.

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

Multiply -1 and 2+3i to get -2-3i.

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

Do the additions in 1+3i+\left(-2-3i\right).

$$2y=x-1$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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