Solve (3x-4)(y-3)=(3y-7)(x-2)

$$(3x-4)(y-3)=(3y-7)(x-2)$$

Solve for x

$$x=y-1$$

Steps for Solving Linear Equation

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

$$3xy-9x-4y+12=\left(3y-7\right)\left(x-2\right)$$

Use the distributive property to multiply 3y-7 by x-2.

$$3xy-9x-4y+12=3yx-6y-7x+14$$

Subtract 3yx from both sides.

$$3xy-9x-4y+12-3yx=-6y-7x+14$$

Combine 3xy and -3yx to get 0.

$$-9x-4y+12=-6y-7x+14$$

Add 7x to both sides.

$$-9x-4y+12+7x=-6y+14$$

Combine -9x and 7x to get -2x.

$$-2x-4y+12=-6y+14$$

Add 4y to both sides.

$$-2x+12=-6y+14+4y$$

Combine -6y and 4y to get -2y.

$$-2x+12=-2y+14$$

Subtract 12 from both sides.

$$-2x=-2y+14-12$$

Subtract 12 from 14 to get 2.

$$-2x=-2y+2$$

The equation is in standard form.

$$-2x=2-2y$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{2-2y}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{2-2y}{-2}$$

Divide -2y+2 by -2.

$$x=y-1$$

Solve for y

$$y=x+1$$

Steps for Solving Linear Equation

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

$$3xy-9x-4y+12=\left(3y-7\right)\left(x-2\right)$$

Use the distributive property to multiply 3y-7 by x-2.

$$3xy-9x-4y+12=3yx-6y-7x+14$$

Subtract 3yx from both sides.

$$3xy-9x-4y+12-3yx=-6y-7x+14$$

Combine 3xy and -3yx to get 0.

$$-9x-4y+12=-6y-7x+14$$

Add 6y to both sides.

$$-9x-4y+12+6y=-7x+14$$

Combine -4y and 6y to get 2y.

$$-9x+2y+12=-7x+14$$

Add 9x to both sides.

$$2y+12=-7x+14+9x$$

Combine -7x and 9x to get 2x.

$$2y+12=2x+14$$

Subtract 12 from both sides.

$$2y=2x+14-12$$

Subtract 12 from 14 to get 2.

$$2y=2x+2$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{2x+2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{2x+2}{2}$$

Divide 2+2x by 2.

$$y=x+1$$