Solve 5xy=1/5xy+44/5xy

$$5xy = \frac{ 1 }{ 5 } xy+4 \frac{ 4 }{ 5 } xy$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Multiply both sides of the equation by 5.

$$25xy=1xy+\left(4\times 5+4\right)xy$$

Multiply 4 and 5 to get 20.

$$25xy=1xy+\left(20+4\right)xy$$

Add 20 and 4 to get 24.

$$25xy=1xy+24xy$$

Combine 1xy and 24xy to get 25xy.

$$25xy=25xy$$

Subtract 25xy from both sides.

$$25xy-25xy=0$$

Combine 25xy and -25xy to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

Multiply both sides of the equation by 5.

$$25xy=1xy+\left(4\times 5+4\right)xy$$

Multiply 4 and 5 to get 20.

$$25xy=1xy+\left(20+4\right)xy$$

Add 20 and 4 to get 24.

$$25xy=1xy+24xy$$

Combine 1xy and 24xy to get 25xy.

$$25xy=25xy$$

Subtract 25xy from both sides.

$$25xy-25xy=0$$

Combine 25xy and -25xy to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 5.

$$25xy=1xy+\left(4\times 5+4\right)xy$$

Multiply 4 and 5 to get 20.

$$25xy=1xy+\left(20+4\right)xy$$

Add 20 and 4 to get 24.

$$25xy=1xy+24xy$$

Combine 1xy and 24xy to get 25xy.

$$25xy=25xy$$

Subtract 25xy from both sides.

$$25xy-25xy=0$$

Combine 25xy and -25xy to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 5.

$$25xy=1xy+\left(4\times 5+4\right)xy$$

Multiply 4 and 5 to get 20.

$$25xy=1xy+\left(20+4\right)xy$$

Add 20 and 4 to get 24.

$$25xy=1xy+24xy$$

Combine 1xy and 24xy to get 25xy.

$$25xy=25xy$$

Subtract 25xy from both sides.

$$25xy-25xy=0$$

Combine 25xy and -25xy to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$