Solve 4/x+10/y=1

$$\frac { 4 } { x } + \frac { 10 } { y } = 1$$

Solve for x

$$x=-\frac{4y}{10-y}$$

$$y\neq 0\text{ and }y\neq 10$$

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.

$$y\times 4+x\times 10=xy$$

Subtract xy from both sides.

$$y\times 4+x\times 10-xy=0$$

Subtract y\times 4 from both sides. Anything subtracted from zero gives its negation.

$$x\times 10-xy=-y\times 4$$

Multiply -1 and 4 to get -4.

$$x\times 10-xy=-4y$$

Combine all terms containing x.

$$\left(10-y\right)x=-4y$$

Divide both sides by 10-y.

$$\frac{\left(10-y\right)x}{10-y}=-\frac{4y}{10-y}$$

Dividing by 10-y undoes the multiplication by 10-y.

$$x=-\frac{4y}{10-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{4y}{10-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{10x}{4-x}$$

$$x\neq 0\text{ and }x\neq 4$$

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.

$$y\times 4+x\times 10=xy$$

Subtract xy from both sides.

$$y\times 4+x\times 10-xy=0$$

Subtract x\times 10 from both sides. Anything subtracted from zero gives its negation.

$$y\times 4-xy=-x\times 10$$

Multiply -1 and 10 to get -10.

$$y\times 4-xy=-10x$$

Combine all terms containing y.

$$\left(4-x\right)y=-10x$$

Divide both sides by 4-x.

$$\frac{\left(4-x\right)y}{4-x}=-\frac{10x}{4-x}$$

Dividing by 4-x undoes the multiplication by 4-x.

$$y=-\frac{10x}{4-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{10x}{4-x}\text{, }y\neq 0$$