Solve 2x-ileft(2+iright)=4-yi

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

Solve for x

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

Steps for Solving Linear Equation

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

$$2x-\left(-1+2i\right)=4-yi$$

Add -1+2i to both sides.

$$2x=4-yi+\left(-1+2i\right)$$

Do the additions in 4+\left(-1+2i\right).

$$2x=-yi+3+2i$$

Multiply -1 and i to get -i.

$$2x=-iy+3+2i$$

The equation is in standard form.

$$2x=3+2i-iy$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

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

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

Solve for y

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

Steps for Solving Linear Equation

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

$$2x-\left(-1+2i\right)=4-yi$$

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

$$4-yi=2x-\left(-1+2i\right)$$

Multiply -1 and i to get -i.

$$4-iy=2x-\left(-1+2i\right)$$

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

$$4-iy=2x+\left(1-2i\right)$$

Subtract 4 from both sides.

$$-iy=2x+\left(1-2i\right)-4$$

Do the additions in 1-2i-4.

$$-iy=2x-3-2i$$

The equation is in standard form.

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

Divide both sides by -i.

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

Dividing by -i undoes the multiplication by -i.

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

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

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