Solve x+y/x=7/3

$$\frac { x + y } { x } = \frac { 7 } { 3 }$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of x,3.

$$3\left(x+y\right)=7x$$

Use the distributive property to multiply 3 by x+y.

$$3x+3y=7x$$

Subtract 7x from both sides.

$$3x+3y-7x=0$$

Combine 3x and -7x to get -4x.

$$-4x+3y=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$-4x=-3y$$

Divide both sides by -4.

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

Dividing by -4 undoes the multiplication by -4.

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

Divide -3y by -4.

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

Variable x cannot be equal to 0.

$$x=\frac{3y}{4}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$3\left(x+y\right)=7x$$

Use the distributive property to multiply 3 by x+y.

$$3x+3y=7x$$

Subtract 3x from both sides.

$$3y=7x-3x$$

Combine 7x and -3x to get 4x.

$$3y=4x$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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