Solve -4+16i+7x=9-8i+10yi

$$- 4 + 16 i + 7 x = 9 - 8 i + 10 y i$$

Solve for x

$$x=\frac{10iy}{7}+\left(\frac{13}{7}-\frac{24}{7}i\right)$$

Steps for Solving Linear Equation

Multiply 10 and i to get 10i.

$$-4+16i+7x=9-8i+10iy$$

Subtract -4+16i from both sides.

$$7x=9-8i+10iy-\left(-4+16i\right)$$

Multiply -1 and -4+16i to get 4-16i.

$$7x=9-8i+10iy+\left(4-16i\right)$$

Do the additions in 9-8i+\left(4-16i\right).

$$7x=10iy+13-24i$$

The equation is in standard form.

$$7x=10iy+\left(13-24i\right)$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{10iy+\left(13-24i\right)}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{10iy+\left(13-24i\right)}{7}$$

Divide 10iy+\left(13-24i\right) by 7.

$$x=\frac{10iy}{7}+\left(\frac{13}{7}-\frac{24}{7}i\right)$$

Solve for y

$$y=-\frac{7ix}{10}+\left(\frac{12}{5}+\frac{13}{10}i\right)$$

Steps for Solving Linear Equation

Multiply 10 and i to get 10i.

$$-4+16i+7x=9-8i+10iy$$

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

$$9-8i+10iy=-4+16i+7x$$

Subtract 9-8i from both sides.

$$10iy=-4+16i+7x-\left(9-8i\right)$$

Multiply -1 and 9-8i to get -9+8i.

$$10iy=-4+16i+7x+\left(-9+8i\right)$$

Do the additions in -4+16i+\left(-9+8i\right).

$$10iy=7x-13+24i$$

The equation is in standard form.

$$10iy=7x+\left(-13+24i\right)$$

Divide both sides by 10i.

$$\frac{10iy}{10i}=\frac{7x+\left(-13+24i\right)}{10i}$$

Dividing by 10i undoes the multiplication by 10i.

$$y=\frac{7x+\left(-13+24i\right)}{10i}$$

Divide 7x+\left(-13+24i\right) by 10i.

$$y=-\frac{7ix}{10}+\left(\frac{12}{5}+\frac{13}{10}i\right)$$