Solve 3x+1/2y=x

$$3 x + \frac { 1 } { 2 y } = x$$

Solve for x

$$x=-\frac{1}{4y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y.

$$3x\times 2y+1=x\times 2y$$

Multiply 3 and 2 to get 6.

$$6xy+1=x\times 2y$$

Subtract x\times 2y from both sides.

$$6xy+1-x\times 2y=0$$

Combine 6xy and -x\times 2y to get 4xy.

$$4xy+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$4xy=-1$$

The equation is in standard form.

$$4yx=-1$$

Divide both sides by 4y.

$$\frac{4yx}{4y}=-\frac{1}{4y}$$

Dividing by 4y undoes the multiplication by 4y.

$$x=-\frac{1}{4y}$$

Solve for y

$$y=-\frac{1}{4x}$$

$$x\neq 0$$

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 2y.

$$3x\times 2y+1=x\times 2y$$

Multiply 3 and 2 to get 6.

$$6xy+1=x\times 2y$$

Subtract x\times 2y from both sides.

$$6xy+1-x\times 2y=0$$

Combine 6xy and -x\times 2y to get 4xy.

$$4xy+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$4xy=-1$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=-\frac{1}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=-\frac{1}{4x}$$

Variable y cannot be equal to 0.

$$y=-\frac{1}{4x}\text{, }y\neq 0$$