Solve (2i-5)x+3iy=-5-4i

$$( 2 i - 5 ) x + 3 i y = - 5 - 4 i$$

Solve for x

$$x=\left(-\frac{6}{29}+\frac{15}{29}i\right)y+\left(\frac{17}{29}+\frac{30}{29}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2i-5 by x.

$$\left(-5+2i\right)x+3iy=-5-4i$$

Subtract 3iy from both sides.

$$\left(-5+2i\right)x=-5-4i-3iy$$

Divide both sides by -5+2i.

$$\frac{\left(-5+2i\right)x}{-5+2i}=\frac{-5-4i-3iy}{-5+2i}$$

Dividing by -5+2i undoes the multiplication by -5+2i.

$$x=\frac{-5-4i-3iy}{-5+2i}$$

Divide -5-4i-3iy by -5+2i.

$$x=\left(-\frac{6}{29}+\frac{15}{29}i\right)y+\left(\frac{17}{29}+\frac{30}{29}i\right)$$

Solve for y

$$y=\left(-\frac{2}{3}-\frac{5}{3}i\right)x+\left(-\frac{4}{3}+\frac{5}{3}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2i-5 by x.

$$\left(-5+2i\right)x+3iy=-5-4i$$

Subtract \left(-5+2i\right)x from both sides.

$$3iy=-5-4i-\left(-5+2i\right)x$$

Multiply -1 and -5+2i to get 5-2i.

$$3iy=-5-4i+\left(5-2i\right)x$$

The equation is in standard form.

$$3iy=\left(5-2i\right)x+\left(-5-4i\right)$$

Divide both sides by 3i.

$$\frac{3iy}{3i}=\frac{\left(5-2i\right)x+\left(-5-4i\right)}{3i}$$

Dividing by 3i undoes the multiplication by 3i.

$$y=\frac{\left(5-2i\right)x+\left(-5-4i\right)}{3i}$$

Divide -5-4i+\left(5-2i\right)x by 3i.

$$y=\left(-\frac{2}{3}-\frac{5}{3}i\right)x+\left(-\frac{4}{3}+\frac{5}{3}i\right)$$