Solve 5/x+2/y=7/z

$$\frac{ 5 }{ x } + \frac{ 2 }{ y } = \frac{ 7 }{ z }$$

Solve for x

$$x=-\frac{5yz}{2z-7y}$$

$$z\neq 0\text{ and }y\neq 0\text{ and }y\neq \frac{2z}{7}$$

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 xyz, the least common multiple of x,y,z.

$$yz\times 5+xz\times 2=xy\times 7$$

Subtract xy\times 7 from both sides.

$$yz\times 5+xz\times 2-xy\times 7=0$$

Multiply -1 and 7 to get -7.

$$yz\times 5+xz\times 2-7xy=0$$

Subtract yz\times 5 from both sides. Anything subtracted from zero gives its negation.

$$xz\times 2-7xy=-yz\times 5$$

Combine all terms containing x.

$$\left(z\times 2-7y\right)x=-yz\times 5$$

The equation is in standard form.

$$\left(2z-7y\right)x=-5yz$$

Divide both sides by 2z-7y.

$$\frac{\left(2z-7y\right)x}{2z-7y}=-\frac{5yz}{2z-7y}$$

Dividing by 2z-7y undoes the multiplication by 2z-7y.

$$x=-\frac{5yz}{2z-7y}$$

Variable x cannot be equal to 0.

$$x=-\frac{5yz}{2z-7y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2xz}{5z-7x}$$

$$z\neq 0\text{ and }x\neq 0\text{ and }x\neq \frac{5z}{7}$$

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 xyz, the least common multiple of x,y,z.

$$yz\times 5+xz\times 2=xy\times 7$$

Subtract xy\times 7 from both sides.

$$yz\times 5+xz\times 2-xy\times 7=0$$

Multiply -1 and 7 to get -7.

$$yz\times 5+xz\times 2-7xy=0$$

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

$$yz\times 5-7xy=-xz\times 2$$

Combine all terms containing y.

$$\left(z\times 5-7x\right)y=-xz\times 2$$

The equation is in standard form.

$$\left(5z-7x\right)y=-2xz$$

Divide both sides by 5z-7x.

$$\frac{\left(5z-7x\right)y}{5z-7x}=-\frac{2xz}{5z-7x}$$

Dividing by 5z-7x undoes the multiplication by 5z-7x.

$$y=-\frac{2xz}{5z-7x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2xz}{5z-7x}\text{, }y\neq 0$$