Solve y/x_{1}+y/x_{2}=7

$$\frac { y } { x _ { 1 } } + \frac { y } { x _ { 2 } } = 7$$

Solve for x_1

$$x_{1}=-\frac{x_{2}y}{y-7x_{2}}$$

$$x_{2}\neq 0\text{ and }y\neq 0\text{ and }y\neq 7x_{2}$$

Steps for Solving Linear Equation

Variable x_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x_{1}x_{2}, the least common multiple of x_{1},x_{2}.

$$x_{2}y+x_{1}y=7x_{1}x_{2}$$

Subtract 7x_{1}x_{2} from both sides.

$$x_{2}y+x_{1}y-7x_{1}x_{2}=0$$

Subtract x_{2}y from both sides. Anything subtracted from zero gives its negation.

$$x_{1}y-7x_{1}x_{2}=-x_{2}y$$

Reorder the terms.

$$-7x_{1}x_{2}+x_{1}y=-x_{2}y$$

Combine all terms containing x_{1}.

$$\left(-7x_{2}+y\right)x_{1}=-x_{2}y$$

The equation is in standard form.

$$\left(y-7x_{2}\right)x_{1}=-x_{2}y$$

Divide both sides by y-7x_{2}.

$$\frac{\left(y-7x_{2}\right)x_{1}}{y-7x_{2}}=-\frac{x_{2}y}{y-7x_{2}}$$

Dividing by y-7x_{2} undoes the multiplication by y-7x_{2}.

$$x_{1}=-\frac{x_{2}y}{y-7x_{2}}$$

Variable x_{1} cannot be equal to 0.

$$x_{1}=-\frac{x_{2}y}{y-7x_{2}}\text{, }x_{1}\neq 0$$

Solve for x_2

$$x_{2}=-\frac{x_{1}y}{y-7x_{1}}$$

$$x_{1}\neq 0\text{ and }y\neq 0\text{ and }y\neq 7x_{1}$$

Steps for Solving Linear Equation

Variable x_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x_{1}x_{2}, the least common multiple of x_{1},x_{2}.

$$x_{2}y+x_{1}y=7x_{1}x_{2}$$

Subtract 7x_{1}x_{2} from both sides.

$$x_{2}y+x_{1}y-7x_{1}x_{2}=0$$

Subtract x_{1}y from both sides. Anything subtracted from zero gives its negation.

$$x_{2}y-7x_{1}x_{2}=-x_{1}y$$

Reorder the terms.

$$-7x_{1}x_{2}+x_{2}y=-x_{1}y$$

Combine all terms containing x_{2}.

$$\left(-7x_{1}+y\right)x_{2}=-x_{1}y$$

The equation is in standard form.

$$\left(y-7x_{1}\right)x_{2}=-x_{1}y$$

Divide both sides by y-7x_{1}.

$$\frac{\left(y-7x_{1}\right)x_{2}}{y-7x_{1}}=-\frac{x_{1}y}{y-7x_{1}}$$

Dividing by y-7x_{1} undoes the multiplication by y-7x_{1}.

$$x_{2}=-\frac{x_{1}y}{y-7x_{1}}$$

Variable x_{2} cannot be equal to 0.

$$x_{2}=-\frac{x_{1}y}{y-7x_{1}}\text{, }x_{2}\neq 0$$