Solve x^2y-5x^2y=(1-5)x^2y

$$x ^ { 2 } y - 5 x ^ { 2 } y = ( 1 - 5 ) x ^ { 2 } y$$

Solve for x (complex solution)

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

Solution Steps

Combine x^{2}y and -5x^{2}y to get -4x^{2}y.

$$-4x^{2}y=\left(1-5\right)x^{2}y$$

Subtract 5 from 1 to get -4.

$$-4x^{2}y=-4x^{2}y$$

Add 4x^{2}y to both sides.

$$-4x^{2}y+4x^{2}y=0$$

Combine -4x^{2}y and 4x^{2}y 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

Combine x^{2}y and -5x^{2}y to get -4x^{2}y.

$$-4x^{2}y=\left(1-5\right)x^{2}y$$

Subtract 5 from 1 to get -4.

$$-4x^{2}y=-4x^{2}y$$

Add 4x^{2}y to both sides.

$$-4x^{2}y+4x^{2}y=0$$

Combine -4x^{2}y and 4x^{2}y 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

Combine x^{2}y and -5x^{2}y to get -4x^{2}y.

$$-4x^{2}y=\left(1-5\right)x^{2}y$$

Subtract 5 from 1 to get -4.

$$-4x^{2}y=-4x^{2}y$$

Add 4x^{2}y to both sides.

$$-4x^{2}y+4x^{2}y=0$$

Combine -4x^{2}y and 4x^{2}y 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

Combine x^{2}y and -5x^{2}y to get -4x^{2}y.

$$-4x^{2}y=\left(1-5\right)x^{2}y$$

Subtract 5 from 1 to get -4.

$$-4x^{2}y=-4x^{2}y$$

Add 4x^{2}y to both sides.

$$-4x^{2}y+4x^{2}y=0$$

Combine -4x^{2}y and 4x^{2}y to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any y.

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