Solve (1+i)x-(1-2i)y=1+4i

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

Solve for x

$$x=\left(-\frac{1}{2}-\frac{3}{2}i\right)y+\left(\frac{5}{2}+\frac{3}{2}i\right)$$

Steps for Solving Linear Equation

Add \left(1-2i\right)y to both sides.

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

The equation is in standard form.

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

Divide both sides by 1+i.

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

Dividing by 1+i undoes the multiplication by 1+i.

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

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

$$x=\left(-\frac{1}{2}-\frac{3}{2}i\right)y+\left(\frac{5}{2}+\frac{3}{2}i\right)$$

Solve for y

$$y=\left(-\frac{1}{5}+\frac{3}{5}i\right)x+\left(\frac{7}{5}-\frac{6}{5}i\right)$$

Steps for Solving Linear Equation

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

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

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

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

The equation is in standard form.

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

Divide both sides by -1+2i.

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

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

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

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

$$y=\left(-\frac{1}{5}+\frac{3}{5}i\right)x+\left(\frac{7}{5}-\frac{6}{5}i\right)$$