Solve 2(x+y/6)+2(x-y/3)=14/28

$$2 ( \frac { x + y } { 6 } ) + 2 ( \frac { x - y } { 3 } ) = \frac { 14 } { 28 }$$

Solve for x

$$x=\frac{y}{3}+\frac{1}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 84, the least common multiple of 6,3,28.

$$28\left(x+y\right)+56\left(x-y\right)=3\times 14$$

Use the distributive property to multiply 28 by x+y.

$$28x+28y+56\left(x-y\right)=3\times 14$$

Use the distributive property to multiply 56 by x-y.

$$28x+28y+56x-56y=3\times 14$$

Combine 28x and 56x to get 84x.

$$84x+28y-56y=3\times 14$$

Combine 28y and -56y to get -28y.

$$84x-28y=3\times 14$$

Multiply 3 and 14 to get 42.

$$84x-28y=42$$

Add 28y to both sides.

$$84x=42+28y$$

The equation is in standard form.

$$84x=28y+42$$

Divide both sides by 84.

$$\frac{84x}{84}=\frac{28y+42}{84}$$

Dividing by 84 undoes the multiplication by 84.

$$x=\frac{28y+42}{84}$$

Divide 42+28y by 84.

$$x=\frac{y}{3}+\frac{1}{2}$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 84, the least common multiple of 6,3,28.

$$28\left(x+y\right)+56\left(x-y\right)=3\times 14$$

Use the distributive property to multiply 28 by x+y.

$$28x+28y+56\left(x-y\right)=3\times 14$$

Use the distributive property to multiply 56 by x-y.

$$28x+28y+56x-56y=3\times 14$$

Combine 28x and 56x to get 84x.

$$84x+28y-56y=3\times 14$$

Combine 28y and -56y to get -28y.

$$84x-28y=3\times 14$$

Multiply 3 and 14 to get 42.

$$84x-28y=42$$

Subtract 84x from both sides.

$$-28y=42-84x$$

Divide both sides by -28.

$$\frac{-28y}{-28}=\frac{42-84x}{-28}$$

Dividing by -28 undoes the multiplication by -28.

$$y=\frac{42-84x}{-28}$$

Divide 42-84x by -28.

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