Solve x-y/x-5=3/7

$$\frac { x - y } { x - 5 } = \frac { 3 } { 7 }$$

Solve for x

$$x=\frac{7y-15}{4}$$

$$y\neq 5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 7\left(x-5\right), the least common multiple of x-5,7.

$$7\left(x-y\right)=3\left(x-5\right)$$

Use the distributive property to multiply 7 by x-y.

$$7x-7y=3\left(x-5\right)$$

Use the distributive property to multiply 3 by x-5.

$$7x-7y=3x-15$$

Subtract 3x from both sides.

$$7x-7y-3x=-15$$

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

$$4x-7y=-15$$

Add 7y to both sides.

$$4x=-15+7y$$

The equation is in standard form.

$$4x=7y-15$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{7y-15}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{7y-15}{4}$$

Variable x cannot be equal to 5.

$$x=\frac{7y-15}{4}\text{, }x\neq 5$$

Solve for y

$$y=\frac{4x+15}{7}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7\left(x-5\right), the least common multiple of x-5,7.

$$7\left(x-y\right)=3\left(x-5\right)$$

Use the distributive property to multiply 7 by x-y.

$$7x-7y=3\left(x-5\right)$$

Use the distributive property to multiply 3 by x-5.

$$7x-7y=3x-15$$

Subtract 7x from both sides.

$$-7y=3x-15-7x$$

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

$$-7y=-4x-15$$

Divide both sides by -7.

$$\frac{-7y}{-7}=\frac{-4x-15}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$y=\frac{-4x-15}{-7}$$

Divide -4x-15 by -7.

$$y=\frac{4x+15}{7}$$