Solve 7/2x+1+13/y+2=27

$$\frac{ 7 }{ 2x+1 } + \frac{ 13 }{ y+2 } =27$$

Solve for x

$$x=-\frac{20y+27}{2\left(27y+41\right)}$$

$$y\neq -2\text{ and }y\neq -\frac{41}{27}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(y+2\right)\left(2x+1\right), the least common multiple of 2x+1,y+2.

$$\left(y+2\right)\times 7+\left(2x+1\right)\times 13=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply y+2 by 7.

$$7y+14+\left(2x+1\right)\times 13=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply 2x+1 by 13.

$$7y+14+26x+13=27\left(y+2\right)\left(2x+1\right)$$

Add 14 and 13 to get 27.

$$7y+27+26x=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply 27 by y+2.

$$7y+27+26x=\left(27y+54\right)\left(2x+1\right)$$

Use the distributive property to multiply 27y+54 by 2x+1.

$$7y+27+26x=54yx+27y+108x+54$$

Subtract 54yx from both sides.

$$7y+27+26x-54yx=27y+108x+54$$

Subtract 108x from both sides.

$$7y+27+26x-54yx-108x=27y+54$$

Combine 26x and -108x to get -82x.

$$7y+27-82x-54yx=27y+54$$

Subtract 7y from both sides.

$$27-82x-54yx=27y+54-7y$$

Combine 27y and -7y to get 20y.

$$27-82x-54yx=20y+54$$

Subtract 27 from both sides.

$$-82x-54yx=20y+54-27$$

Subtract 27 from 54 to get 27.

$$-82x-54yx=20y+27$$

Combine all terms containing x.

$$\left(-82-54y\right)x=20y+27$$

The equation is in standard form.

$$\left(-54y-82\right)x=20y+27$$

Divide both sides by -82-54y.

$$\frac{\left(-54y-82\right)x}{-54y-82}=\frac{20y+27}{-54y-82}$$

Dividing by -82-54y undoes the multiplication by -82-54y.

$$x=\frac{20y+27}{-54y-82}$$

Divide 20y+27 by -82-54y.

$$x=-\frac{20y+27}{2\left(27y+41\right)}$$

Variable x cannot be equal to -\frac{1}{2}.

$$x=-\frac{20y+27}{2\left(27y+41\right)}\text{, }x\neq -\frac{1}{2}$$

Solve for y

$$y=-\frac{82x+27}{2\left(27x+10\right)}$$

$$x\neq -\frac{1}{2}\text{ and }x\neq -\frac{10}{27}$$

Steps for Solving Linear Equation

Variable y cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by \left(y+2\right)\left(2x+1\right), the least common multiple of 2x+1,y+2.

$$\left(y+2\right)\times 7+\left(2x+1\right)\times 13=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply y+2 by 7.

$$7y+14+\left(2x+1\right)\times 13=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply 2x+1 by 13.

$$7y+14+26x+13=27\left(y+2\right)\left(2x+1\right)$$

Add 14 and 13 to get 27.

$$7y+27+26x=27\left(y+2\right)\left(2x+1\right)$$

Use the distributive property to multiply 27 by y+2.

$$7y+27+26x=\left(27y+54\right)\left(2x+1\right)$$

Use the distributive property to multiply 27y+54 by 2x+1.

$$7y+27+26x=54yx+27y+108x+54$$

Subtract 54yx from both sides.

$$7y+27+26x-54yx=27y+108x+54$$

Subtract 27y from both sides.

$$7y+27+26x-54yx-27y=108x+54$$

Combine 7y and -27y to get -20y.

$$-20y+27+26x-54yx=108x+54$$

Subtract 27 from both sides.

$$-20y+26x-54yx=108x+54-27$$

Subtract 27 from 54 to get 27.

$$-20y+26x-54yx=108x+27$$

Subtract 26x from both sides.

$$-20y-54yx=108x+27-26x$$

Combine 108x and -26x to get 82x.

$$-20y-54yx=82x+27$$

Combine all terms containing y.

$$\left(-20-54x\right)y=82x+27$$

The equation is in standard form.

$$\left(-54x-20\right)y=82x+27$$

Divide both sides by -54x-20.

$$\frac{\left(-54x-20\right)y}{-54x-20}=\frac{82x+27}{-54x-20}$$

Dividing by -54x-20 undoes the multiplication by -54x-20.

$$y=\frac{82x+27}{-54x-20}$$

Divide 27+82x by -54x-20.

$$y=-\frac{82x+27}{2\left(27x+10\right)}$$

Variable y cannot be equal to -2.

$$y=-\frac{82x+27}{2\left(27x+10\right)}\text{, }y\neq -2$$