Solve 2/x+3/y=-1

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

Solve for x

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

$$y\neq 0\text{ and }y\neq -3$$

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 xy, the least common multiple of x,y.

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

Add xy to both sides.

$$y\times 2+x\times 3+xy=0$$

Subtract y\times 2 from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and 2 to get -2.

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

Combine all terms containing x.

$$\left(3+y\right)x=-2y$$

The equation is in standard form.

$$\left(y+3\right)x=-2y$$

Divide both sides by y+3.

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

Dividing by y+3 undoes the multiplication by y+3.

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

Variable x cannot be equal to 0.

$$x=-\frac{2y}{y+3}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0\text{ and }x\neq -2$$

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 xy, the least common multiple of x,y.

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

Add xy to both sides.

$$y\times 2+x\times 3+xy=0$$

Subtract x\times 3 from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and 3 to get -3.

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

Combine all terms containing y.

$$\left(2+x\right)y=-3x$$

The equation is in standard form.

$$\left(x+2\right)y=-3x$$

Divide both sides by x+2.

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

Dividing by x+2 undoes the multiplication by x+2.

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

Variable y cannot be equal to 0.

$$y=-\frac{3x}{x+2}\text{, }y\neq 0$$