Solve 1/4x+1/2y=4

$$\frac { 1 } { 4 x } + \frac { 1 } { 2 y } = 4$$

Solve for x

$$x=-\frac{y}{2\left(1-8y\right)}$$

$$y\neq 0\text{ and }y\neq \frac{1}{8}$$

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 4xy, the least common multiple of 4x,2y.

$$y+2x=16xy$$

Subtract 16xy from both sides.

$$y+2x-16xy=0$$

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

$$2x-16xy=-y$$

Combine all terms containing x.

$$\left(2-16y\right)x=-y$$

Divide both sides by -16y+2.

$$\frac{\left(2-16y\right)x}{2-16y}=-\frac{y}{2-16y}$$

Dividing by -16y+2 undoes the multiplication by -16y+2.

$$x=-\frac{y}{2-16y}$$

Divide -y by -16y+2.

$$x=-\frac{y}{2\left(1-8y\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{2\left(1-8y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2x}{1-16x}$$

$$x\neq 0\text{ and }x\neq \frac{1}{16}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4xy, the least common multiple of 4x,2y.

$$y+2x=16xy$$

Subtract 16xy from both sides.

$$y+2x-16xy=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$y-16xy=-2x$$

Combine all terms containing y.

$$\left(1-16x\right)y=-2x$$

Divide both sides by 1-16x.

$$\frac{\left(1-16x\right)y}{1-16x}=-\frac{2x}{1-16x}$$

Dividing by 1-16x undoes the multiplication by 1-16x.

$$y=-\frac{2x}{1-16x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2x}{1-16x}\text{, }y\neq 0$$