Solve yx/5-x-y/3=2pi

$$y \frac { x } { 5 } - \frac { x - y } { 3 } = 2 \pi$$

Solve for x

$$x=-\frac{5\left(y-6\pi \right)}{3y-5}$$

$$y\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3yx-5\left(x-y\right)=30\pi$$

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

$$3yx-5x+5y=30\pi$$

Subtract 5y from both sides.

$$3yx-5x=30\pi -5y$$

Combine all terms containing x.

$$\left(3y-5\right)x=30\pi -5y$$

Divide both sides by 3y-5.

$$\frac{\left(3y-5\right)x}{3y-5}=\frac{30\pi -5y}{3y-5}$$

Dividing by 3y-5 undoes the multiplication by 3y-5.

$$x=\frac{30\pi -5y}{3y-5}$$

Divide 30\pi -5y by 3y-5.

$$x=\frac{5\left(6\pi -y\right)}{3y-5}$$

Solve for y

$$y=\frac{5\left(x+6\pi \right)}{3x+5}$$

$$x\neq -\frac{5}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3yx-5\left(x-y\right)=30\pi$$

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

$$3yx-5x+5y=30\pi$$

Add 5x to both sides.

$$3yx+5y=30\pi +5x$$

Combine all terms containing y.

$$\left(3x+5\right)y=30\pi +5x$$

The equation is in standard form.

$$\left(3x+5\right)y=5x+30\pi$$

Divide both sides by 3x+5.

$$\frac{\left(3x+5\right)y}{3x+5}=\frac{5x+30\pi }{3x+5}$$

Dividing by 3x+5 undoes the multiplication by 3x+5.

$$y=\frac{5x+30\pi }{3x+5}$$

Divide 30\pi +5x by 3x+5.

$$y=\frac{5\left(x+6\pi \right)}{3x+5}$$