Solve -7i^8x-4i+y=-5i^19y-4x

$$-7 { i }^{ 8 } x-4i+y = -5 { i }^{ 19 } y-4x$$

Solve for x

$$x=\left(\frac{1}{3}-\frac{5}{3}i\right)y-\frac{4}{3}i$$

Steps for Solving Linear Equation

Calculate i to the power of 8 and get 1.

$$-7x-4i+y=-5i^{19}y-4x$$

Calculate i to the power of 19 and get -i.

$$-7x-4i+y=-5\left(-i\right)y-4x$$

Multiply -5 and -i to get 5i.

$$-7x-4i+y=5iy-4x$$

Add 4x to both sides.

$$-7x-4i+y+4x=5iy$$

Combine -7x and 4x to get -3x.

$$-3x-4i+y=5iy$$

Add 4i to both sides.

$$-3x+y=5iy+4i$$

Subtract y from both sides.

$$-3x=5iy+4i-y$$

Combine 5iy and -y to get \left(-1+5i\right)y.

$$-3x=\left(-1+5i\right)y+4i$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{\left(-1+5i\right)y+4i}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{\left(-1+5i\right)y+4i}{-3}$$

Divide \left(-1+5i\right)y+4i by -3.

$$x=\left(\frac{1}{3}-\frac{5}{3}i\right)y-\frac{4}{3}i$$

Solve for y

$$y=\left(\frac{3}{26}+\frac{15}{26}i\right)x+\left(-\frac{10}{13}+\frac{2}{13}i\right)$$

Steps for Solving Linear Equation

Calculate i to the power of 8 and get 1.

$$-7x-4i+y=-5i^{19}y-4x$$

Calculate i to the power of 19 and get -i.

$$-7x-4i+y=-5\left(-i\right)y-4x$$

Multiply -5 and -i to get 5i.

$$-7x-4i+y=5iy-4x$$

Subtract 5iy from both sides.

$$-7x-4i+y-5iy=-4x$$

Combine y and -5iy to get \left(1-5i\right)y.

$$-7x-4i+\left(1-5i\right)y=-4x$$

Add 7x to both sides.

$$-4i+\left(1-5i\right)y=-4x+7x$$

Combine -4x and 7x to get 3x.

$$-4i+\left(1-5i\right)y=3x$$

Add 4i to both sides.

$$\left(1-5i\right)y=3x+4i$$

Divide both sides by 1-5i.

$$\frac{\left(1-5i\right)y}{1-5i}=\frac{3x+4i}{1-5i}$$

Dividing by 1-5i undoes the multiplication by 1-5i.

$$y=\frac{3x+4i}{1-5i}$$

Divide 3x+4i by 1-5i.

$$y=\left(\frac{3}{26}+\frac{15}{26}i\right)x+\left(-\frac{10}{13}+\frac{2}{13}i\right)$$