Solve 3(x-1)+2y=4(y-3)

$$3 ( x - 1 ) + 2 y = 4 ( y - 3 )$$

Solve for x

$$x=\frac{2y}{3}-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x-1.

$$3x-3+2y=4\left(y-3\right)$$

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

$$3x-3+2y=4y-12$$

Add 3 to both sides.

$$3x+2y=4y-12+3$$

Add -12 and 3 to get -9.

$$3x+2y=4y-9$$

Subtract 2y from both sides.

$$3x=4y-9-2y$$

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

$$3x=2y-9$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2y-9}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2y-9}{3}$$

Divide 2y-9 by 3.

$$x=\frac{2y}{3}-3$$

Solve for y

$$y=\frac{3\left(x+3\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x-1.

$$3x-3+2y=4\left(y-3\right)$$

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

$$3x-3+2y=4y-12$$

Subtract 4y from both sides.

$$3x-3+2y-4y=-12$$

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

$$3x-3-2y=-12$$

Subtract 3x from both sides.

$$-3-2y=-12-3x$$

Add 3 to both sides.

$$-2y=-12-3x+3$$

Add -12 and 3 to get -9.

$$-2y=-9-3x$$

The equation is in standard form.

$$-2y=-3x-9$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{-3x-9}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{-3x-9}{-2}$$

Divide -9-3x by -2.

$$y=\frac{3x+9}{2}$$