Solve x+4/3-y-9/6=9/5

$$\frac { x + 4 } { 3 } - \frac { y - 9 } { 6 } = \frac { 9 } { 5 }$$

Solve for x

$$x=\frac{y}{2}-\frac{31}{10}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,6,5.

$$10\left(x+4\right)-5\left(y-9\right)=54$$

Use the distributive property to multiply 10 by x+4.

$$10x+40-5\left(y-9\right)=54$$

Use the distributive property to multiply -5 by y-9.

$$10x+40-5y+45=54$$

Add 40 and 45 to get 85.

$$10x+85-5y=54$$

Subtract 85 from both sides.

$$10x-5y=54-85$$

Subtract 85 from 54 to get -31.

$$10x-5y=-31$$

Add 5y to both sides.

$$10x=-31+5y$$

The equation is in standard form.

$$10x=5y-31$$

Divide both sides by 10.

$$\frac{10x}{10}=\frac{5y-31}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$x=\frac{5y-31}{10}$$

Divide -31+5y by 10.

$$x=\frac{y}{2}-\frac{31}{10}$$

Solve for y

$$y=2x+\frac{31}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,6,5.

$$10\left(x+4\right)-5\left(y-9\right)=54$$

Use the distributive property to multiply 10 by x+4.

$$10x+40-5\left(y-9\right)=54$$

Use the distributive property to multiply -5 by y-9.

$$10x+40-5y+45=54$$

Add 40 and 45 to get 85.

$$10x+85-5y=54$$

Subtract 10x from both sides.

$$85-5y=54-10x$$

Subtract 85 from both sides.

$$-5y=54-10x-85$$

Subtract 85 from 54 to get -31.

$$-5y=-31-10x$$

The equation is in standard form.

$$-5y=-10x-31$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{-10x-31}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{-10x-31}{-5}$$

Divide -31-10x by -5.

$$y=2x+\frac{31}{5}$$