Solve {l}{2+3i+y=10}{2+x-y=4}

$$\left. \begin{array} { l } { 2 + 3 i + y = 10 } \\ { 2 + x - y = 4 } \end{array} \right.$$

Solve for y, x

$$x=10-3i$$

$$y=8-3i$$

Solution Steps

Consider the first equation. Subtract 2+3i from both sides.

$$y=10-\left(2+3i\right)$$

Subtract 2+3i from 10 to get 8-3i.

$$y=8-3i$$

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

$$2+x-\left(8-3i\right)=4$$

Multiply -1 and 8-3i to get -8+3i.

$$2+x+\left(-8+3i\right)=4$$

Do the additions in 2+\left(-8+3i\right).

$$x-6+3i=4$$

Add 6 to both sides.

$$x+3i=4+6$$

Add 4 and 6 to get 10.

$$x+3i=10$$

Subtract 3i from both sides.

$$x=10-3i$$

The system is now solved.

$$y=8-3i x=10-3i$$