Solve (3-2i)(x-yi)=2(x-2yi)+4i-1

$$( 3 - 2 i ) ( x - y i ) = 2 ( x - 2 y i ) + 4 i - 1$$

Solve for x

$$x=\left(\frac{4}{5}+\frac{3}{5}i\right)y+\left(-\frac{9}{5}+\frac{2}{5}i\right)$$

Steps for Solving Linear Equation

Multiply 2 and i to get 2i.

$$\left(3-2i\right)\left(x-yi\right)=2\left(x-2iy\right)+4i-1$$

Subtract 2\left(x-2iy\right) from both sides.

$$\left(3-2i\right)\left(x-yi\right)-2\left(x-2iy\right)=4i-1$$

Multiply -1 and i to get -i.

$$\left(3-2i\right)\left(x-iy\right)-2\left(x-2iy\right)=4i-1$$

Use the distributive property to multiply 3-2i by x-iy.

$$\left(3-2i\right)x+\left(-2-3i\right)y-2\left(x-2iy\right)=4i-1$$

Use the distributive property to multiply -2 by x-2iy.

$$\left(3-2i\right)x+\left(-2-3i\right)y-2x+4iy=4i-1$$

Combine \left(3-2i\right)x and -2x to get \left(1-2i\right)x.

$$\left(1-2i\right)x+\left(-2-3i\right)y+4iy=4i-1$$

Combine \left(-2-3i\right)y and 4iy to get \left(-2+i\right)y.

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

Subtract \left(-2+i\right)y from both sides.

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

The equation is in standard form.

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

Divide both sides by 1-2i.

$$\frac{\left(1-2i\right)x}{1-2i}=\frac{\left(2-i\right)y+\left(-1+4i\right)}{1-2i}$$

Dividing by 1-2i undoes the multiplication by 1-2i.

$$x=\frac{\left(2-i\right)y+\left(-1+4i\right)}{1-2i}$$

Divide -1+4i+\left(2-i\right)y by 1-2i.

$$x=\left(\frac{4}{5}+\frac{3}{5}i\right)y+\left(-\frac{9}{5}+\frac{2}{5}i\right)$$

Solve for y

$$y=\left(\frac{4}{5}-\frac{3}{5}i\right)x+\left(\frac{6}{5}-\frac{7}{5}i\right)$$

Steps for Solving Linear Equation

Multiply 2 and i to get 2i.

$$\left(3-2i\right)\left(x-yi\right)=2\left(x-2iy\right)+4i-1$$

Subtract 2\left(x-2iy\right) from both sides.

$$\left(3-2i\right)\left(x-yi\right)-2\left(x-2iy\right)=4i-1$$

Multiply -1 and i to get -i.

$$\left(3-2i\right)\left(x-iy\right)-2\left(x-2iy\right)=4i-1$$

Use the distributive property to multiply 3-2i by x-iy.

$$\left(3-2i\right)x+\left(-2-3i\right)y-2\left(x-2iy\right)=4i-1$$

Use the distributive property to multiply -2 by x-2iy.

$$\left(3-2i\right)x+\left(-2-3i\right)y-2x+4iy=4i-1$$

Combine \left(3-2i\right)x and -2x to get \left(1-2i\right)x.

$$\left(1-2i\right)x+\left(-2-3i\right)y+4iy=4i-1$$

Combine \left(-2-3i\right)y and 4iy to get \left(-2+i\right)y.

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

Subtract \left(1-2i\right)x from both sides.

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

The equation is in standard form.

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

Divide both sides by -2+i.

$$\frac{\left(-2+i\right)y}{-2+i}=\frac{\left(-1+2i\right)x+\left(-1+4i\right)}{-2+i}$$

Dividing by -2+i undoes the multiplication by -2+i.

$$y=\frac{\left(-1+2i\right)x+\left(-1+4i\right)}{-2+i}$$

Divide -1+4i+\left(-1+2i\right)x by -2+i.

$$y=\left(\frac{4}{5}-\frac{3}{5}i\right)x+\left(\frac{6}{5}-\frac{7}{5}i\right)$$