Solve 9x-12y=3(3x-4y)

$$9 x - 12 y = 3 ( 3 x - 4 y )$$

Solve for x (complex solution)

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

Solution Steps

Use the distributive property to multiply 3 by 3x-4y.

$$9x-12y=9x-12y$$

Subtract 9x from both sides.

$$9x-12y-9x=-12y$$

Combine 9x and -9x to get 0.

$$-12y=-12y$$

Cancel out -12 on both sides.

$$y=y$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

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

Solve for y (complex solution)

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

Solution Steps

Use the distributive property to multiply 3 by 3x-4y.

$$9x-12y=9x-12y$$

Add 12y to both sides.

$$9x-12y+12y=9x$$

Combine -12y and 12y to get 0.

$$9x=9x$$

Cancel out 9 on both sides.

$$x=x$$

Reorder the terms.

$$\text{true}$$

This is true for any y.

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

Solve for x

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

Solution Steps

Use the distributive property to multiply 3 by 3x-4y.

$$9x-12y=9x-12y$$

Subtract 9x from both sides.

$$9x-12y-9x=-12y$$

Combine 9x and -9x to get 0.

$$-12y=-12y$$

Cancel out -12 on both sides.

$$y=y$$

Reorder the terms.

$$\text{true}$$

This is true for any x.

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

Solve for y

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

Solution Steps

Use the distributive property to multiply 3 by 3x-4y.

$$9x-12y=9x-12y$$

Add 12y to both sides.

$$9x-12y+12y=9x$$

Combine -12y and 12y to get 0.

$$9x=9x$$

Cancel out 9 on both sides.

$$x=x$$

Reorder the terms.

$$\text{true}$$

This is true for any y.

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