Solve 5/x-3-11/y-1=0

$$\frac{ 5 }{ x-3 } - \frac{ 11 }{ y-1 } =0$$

Solve for x

$$x=\frac{5y+28}{11}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(y-1\right), the least common multiple of x-3,y-1.

$$\left(y-1\right)\times 5-\left(x-3\right)\times 11=0$$

Use the distributive property to multiply y-1 by 5.

$$5y-5-\left(x-3\right)\times 11=0$$

Use the distributive property to multiply x-3 by 11.

$$5y-5-\left(11x-33\right)=0$$

To find the opposite of 11x-33, find the opposite of each term.

$$5y-5-11x+33=0$$

Add -5 and 33 to get 28.

$$5y+28-11x=0$$

Subtract 5y from both sides. Anything subtracted from zero gives its negation.

$$28-11x=-5y$$

Subtract 28 from both sides.

$$-11x=-5y-28$$

Divide both sides by -11.

$$\frac{-11x}{-11}=\frac{-5y-28}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$x=\frac{-5y-28}{-11}$$

Divide -5y-28 by -11.

$$x=\frac{5y+28}{11}$$

Variable x cannot be equal to 3.

$$x=\frac{5y+28}{11}\text{, }x\neq 3$$

Solve for y

$$y=\frac{11x-28}{5}$$

$$x\neq 3$$

Steps for Solving Linear Equation

Variable y cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(y-1\right), the least common multiple of x-3,y-1.

$$\left(y-1\right)\times 5-\left(x-3\right)\times 11=0$$

Use the distributive property to multiply y-1 by 5.

$$5y-5-\left(x-3\right)\times 11=0$$

Use the distributive property to multiply x-3 by 11.

$$5y-5-\left(11x-33\right)=0$$

To find the opposite of 11x-33, find the opposite of each term.

$$5y-5-11x+33=0$$

Add -5 and 33 to get 28.

$$5y+28-11x=0$$

Subtract 28 from both sides. Anything subtracted from zero gives its negation.

$$5y-11x=-28$$

Add 11x to both sides.

$$5y=-28+11x$$

The equation is in standard form.

$$5y=11x-28$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{11x-28}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{11x-28}{5}$$

Variable y cannot be equal to 1.

$$y=\frac{11x-28}{5}\text{, }y\neq 1$$