Solve 4x+1/4y+1=5/8

$$\frac { 4 x + 1 } { 4 y + 1 } = \frac { 5 } { 8 }$$

Solve for x

$$x=\frac{5y}{8}-\frac{3}{32}$$

$$y\neq -\frac{1}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8\left(4y+1\right), the least common multiple of 4y+1,8.

$$8\left(4x+1\right)=5\left(4y+1\right)$$

Use the distributive property to multiply 8 by 4x+1.

$$32x+8=5\left(4y+1\right)$$

Use the distributive property to multiply 5 by 4y+1.

$$32x+8=20y+5$$

Subtract 8 from both sides.

$$32x=20y+5-8$$

Subtract 8 from 5 to get -3.

$$32x=20y-3$$

Divide both sides by 32.

$$\frac{32x}{32}=\frac{20y-3}{32}$$

Dividing by 32 undoes the multiplication by 32.

$$x=\frac{20y-3}{32}$$

Divide 20y-3 by 32.

$$x=\frac{5y}{8}-\frac{3}{32}$$

Solve for y

$$y=\frac{8x}{5}+\frac{3}{20}$$

$$x\neq -\frac{1}{4}$$

Steps for Solving Linear Equation

Variable y cannot be equal to -\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by 8\left(4y+1\right), the least common multiple of 4y+1,8.

$$8\left(4x+1\right)=5\left(4y+1\right)$$

Use the distributive property to multiply 8 by 4x+1.

$$32x+8=5\left(4y+1\right)$$

Use the distributive property to multiply 5 by 4y+1.

$$32x+8=20y+5$$

Swap sides so that all variable terms are on the left hand side.

$$20y+5=32x+8$$

Subtract 5 from both sides.

$$20y=32x+8-5$$

Subtract 5 from 8 to get 3.

$$20y=32x+3$$

Divide both sides by 20.

$$\frac{20y}{20}=\frac{32x+3}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$y=\frac{32x+3}{20}$$

Divide 32x+3 by 20.

$$y=\frac{8x}{5}+\frac{3}{20}$$

Variable y cannot be equal to -\frac{1}{4}.

$$y=\frac{8x}{5}+\frac{3}{20}\text{, }y\neq -\frac{1}{4}$$