Solve (2x+i)(4+3i)=(5+yi)

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

Solve for x

$$x=\left(\frac{3}{50}+\frac{2}{25}i\right)y+\left(\frac{2}{5}-\frac{4}{5}i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+i by 4+3i.

$$\left(8+6i\right)x+\left(-3+4i\right)=5+yi$$

Subtract -3+4i from both sides.

$$\left(8+6i\right)x=5+yi-\left(-3+4i\right)$$

Multiply -1 and -3+4i to get 3-4i.

$$\left(8+6i\right)x=5+yi+\left(3-4i\right)$$

Do the additions in 5+\left(3-4i\right).

$$\left(8+6i\right)x=yi+8-4i$$

The equation is in standard form.

$$\left(8+6i\right)x=iy+\left(8-4i\right)$$

Divide both sides by 8+6i.

$$\frac{\left(8+6i\right)x}{8+6i}=\frac{iy+\left(8-4i\right)}{8+6i}$$

Dividing by 8+6i undoes the multiplication by 8+6i.

$$x=\frac{iy+\left(8-4i\right)}{8+6i}$$

Divide iy+\left(8-4i\right) by 8+6i.

$$x=\left(\frac{3}{50}+\frac{2}{25}i\right)y+\left(\frac{2}{5}-\frac{4}{5}i\right)$$

Solve for y

$$y=\left(6-8i\right)x+\left(4+8i\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+i by 4+3i.

$$\left(8+6i\right)x+\left(-3+4i\right)=5+yi$$

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

$$5+yi=\left(8+6i\right)x+\left(-3+4i\right)$$

Subtract 5 from both sides.

$$yi=\left(8+6i\right)x+\left(-3+4i\right)-5$$

Do the additions in -3+4i-5.

$$yi=\left(8+6i\right)x-8+4i$$

The equation is in standard form.

$$iy=\left(8+6i\right)x+\left(-8+4i\right)$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{\left(8+6i\right)x+\left(-8+4i\right)}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{\left(8+6i\right)x+\left(-8+4i\right)}{i}$$

Divide \left(8+6i\right)x+\left(-8+4i\right) by i.

$$y=\left(6-8i\right)x+\left(4+8i\right)$$