Solve 1/2x+2/3y=3

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

Solve for x

$$x=-\frac{3y}{2\left(2-9y\right)}$$

$$y\neq 0\text{ and }y\neq \frac{2}{9}$$

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 6xy, the least common multiple of 2x,3y.

$$3y+2x\times 2=18xy$$

Multiply 2 and 2 to get 4.

$$3y+4x=18xy$$

Subtract 18xy from both sides.

$$3y+4x-18xy=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$4x-18xy=-3y$$

Combine all terms containing x.

$$\left(4-18y\right)x=-3y$$

Divide both sides by -18y+4.

$$\frac{\left(4-18y\right)x}{4-18y}=-\frac{3y}{4-18y}$$

Dividing by -18y+4 undoes the multiplication by -18y+4.

$$x=-\frac{3y}{4-18y}$$

Divide -3y by -18y+4.

$$x=-\frac{3y}{2\left(2-9y\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{3y}{2\left(2-9y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{4x}{3\left(1-6x\right)}$$

$$x\neq 0\text{ and }x\neq \frac{1}{6}$$

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 6xy, the least common multiple of 2x,3y.

$$3y+2x\times 2=18xy$$

Multiply 2 and 2 to get 4.

$$3y+4x=18xy$$

Subtract 18xy from both sides.

$$3y+4x-18xy=0$$

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$3y-18xy=-4x$$

Combine all terms containing y.

$$\left(3-18x\right)y=-4x$$

Divide both sides by -18x+3.

$$\frac{\left(3-18x\right)y}{3-18x}=-\frac{4x}{3-18x}$$

Dividing by -18x+3 undoes the multiplication by -18x+3.

$$y=-\frac{4x}{3-18x}$$

Divide -4x by -18x+3.

$$y=-\frac{4x}{3\left(1-6x\right)}$$

Variable y cannot be equal to 0.

$$y=-\frac{4x}{3\left(1-6x\right)}\text{, }y\neq 0$$