Solve 1/3left(x-yright)=4/1left(y-1right)

$$\frac{ 1 }{ 3 } \left( x-y \right) = \frac{ 4 }{ 1 } \left( y-1 \right)$$

Solve for x

$$x=13y-12$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-y.

$$\frac{1}{3}x-\frac{1}{3}y=\frac{4}{1}\left(y-1\right)$$

Anything divided by one gives itself.

$$\frac{1}{3}x-\frac{1}{3}y=4\left(y-1\right)$$

Use the distributive property to multiply 4 by y-1.

$$\frac{1}{3}x-\frac{1}{3}y=4y-4$$

Add \frac{1}{3}y to both sides.

$$\frac{1}{3}x=4y-4+\frac{1}{3}y$$

Combine 4y and \frac{1}{3}y to get \frac{13}{3}y.

$$\frac{1}{3}x=\frac{13}{3}y-4$$

The equation is in standard form.

$$\frac{1}{3}x=\frac{13y}{3}-4$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}x}{\frac{1}{3}}=\frac{\frac{13y}{3}-4}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$x=\frac{\frac{13y}{3}-4}{\frac{1}{3}}$$

Divide \frac{13y}{3}-4 by \frac{1}{3} by multiplying \frac{13y}{3}-4 by the reciprocal of \frac{1}{3}.

$$x=13y-12$$

Solve for y

$$y=\frac{x+12}{13}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x-y.

$$\frac{1}{3}x-\frac{1}{3}y=\frac{4}{1}\left(y-1\right)$$

Anything divided by one gives itself.

$$\frac{1}{3}x-\frac{1}{3}y=4\left(y-1\right)$$

Use the distributive property to multiply 4 by y-1.

$$\frac{1}{3}x-\frac{1}{3}y=4y-4$$

Subtract 4y from both sides.

$$\frac{1}{3}x-\frac{1}{3}y-4y=-4$$

Combine -\frac{1}{3}y and -4y to get -\frac{13}{3}y.

$$\frac{1}{3}x-\frac{13}{3}y=-4$$

Subtract \frac{1}{3}x from both sides.

$$-\frac{13}{3}y=-4-\frac{1}{3}x$$

The equation is in standard form.

$$-\frac{13}{3}y=-\frac{x}{3}-4$$

Divide both sides of the equation by -\frac{13}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{13}{3}y}{-\frac{13}{3}}=\frac{-\frac{x}{3}-4}{-\frac{13}{3}}$$

Dividing by -\frac{13}{3} undoes the multiplication by -\frac{13}{3}.

$$y=\frac{-\frac{x}{3}-4}{-\frac{13}{3}}$$

Divide -4-\frac{x}{3} by -\frac{13}{3} by multiplying -4-\frac{x}{3} by the reciprocal of -\frac{13}{3}.

$$y=\frac{x+12}{13}$$