Solve {l}{2+(x+y)i=2-i}{x+4i=2+4i}

$$\left\{ \begin{array} { l } { 2 + ( x + y ) i = 2 - i } \\ { x + 4 i = 2 + 4 i } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y=-3$$

Solution Steps

Consider the second equation. Subtract 4i from both sides.

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

Subtract 4i from 2+4i to get 2.

$$x=2$$

Consider the first equation. Insert the known values of variables into the equation.

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

Use the distributive property to multiply 2+y by i.

$$2+2i+iy=2-i$$

Subtract 2 from both sides.

$$2i+iy=2-i-2$$

Subtract 2 from 2-i to get -i.

$$2i+iy=-i$$

Subtract 2i from both sides.

$$iy=-i-2i$$

Subtract 2i from -i to get -3i.

$$iy=-3i$$

Divide both sides by i.

$$y=\frac{-3i}{i}$$

Divide -3i by i to get -3.

$$y=-3$$

The system is now solved.

$$x=2 y=-3$$