Solve 3x/7-x=y/6-y/3

$$\frac { 3 x } { 7 } - x = \frac { y } { 6 } - \frac { y } { 3 }$$

Solve for x

$$x=\frac{7y}{24}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,6,3.

$$6\times 3x-42x=7y-14y$$

Multiply 6 and 3 to get 18.

$$18x-42x=7y-14y$$

Combine 18x and -42x to get -24x.

$$-24x=7y-14y$$

Combine 7y and -14y to get -7y.

$$-24x=-7y$$

Divide both sides by -24.

$$\frac{-24x}{-24}=-\frac{7y}{-24}$$

Dividing by -24 undoes the multiplication by -24.

$$x=-\frac{7y}{-24}$$

Divide -7y by -24.

$$x=\frac{7y}{24}$$

Solve for y

$$y=\frac{24x}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,6,3.

$$6\times 3x-42x=7y-14y$$

Multiply 6 and 3 to get 18.

$$18x-42x=7y-14y$$

Combine 18x and -42x to get -24x.

$$-24x=7y-14y$$

Combine 7y and -14y to get -7y.

$$-24x=-7y$$

Swap sides so that all variable terms are on the left hand side.

$$-7y=-24x$$

Divide both sides by -7.

$$\frac{-7y}{-7}=-\frac{24x}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$y=-\frac{24x}{-7}$$

Divide -24x by -7.

$$y=\frac{24x}{7}$$