Solve 7x+(x-3y)i=3y+9x

$$7 x + ( x - 3 y ) i = 3 y + 9 x$$

Solve for x

$$x=\left(-\frac{3}{5}-\frac{9}{5}i\right)y$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3y by i.

$$7x+ix-3iy=3y+9x$$

Combine 7x and ix to get \left(7+i\right)x.

$$\left(7+i\right)x-3iy=3y+9x$$

Subtract 9x from both sides.

$$\left(7+i\right)x-3iy-9x=3y$$

Combine \left(7+i\right)x and -9x to get \left(-2+i\right)x.

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

Subtract -3iy from both sides.

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

Combine 3y and 3iy to get \left(3+3i\right)y.

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

Divide both sides by -2+i.

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

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

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

Divide \left(3+3i\right)y by -2+i.

$$x=\left(-\frac{3}{5}-\frac{9}{5}i\right)y$$

Solve for y

$$y=\left(-\frac{1}{6}+\frac{1}{2}i\right)x$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-3y by i.

$$7x+ix-3iy=3y+9x$$

Combine 7x and ix to get \left(7+i\right)x.

$$\left(7+i\right)x-3iy=3y+9x$$

Subtract 3y from both sides.

$$\left(7+i\right)x-3iy-3y=9x$$

Combine -3iy and -3y to get \left(-3-3i\right)y.

$$\left(7+i\right)x+\left(-3-3i\right)y=9x$$

Subtract \left(7+i\right)x from both sides.

$$\left(-3-3i\right)y=9x-\left(7+i\right)x$$

Combine 9x and \left(-7-i\right)x to get \left(2-i\right)x.

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

Divide both sides by -3-3i.

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

Dividing by -3-3i undoes the multiplication by -3-3i.

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

Divide \left(2-i\right)x by -3-3i.

$$y=\left(-\frac{1}{6}+\frac{1}{2}i\right)x$$