Solve 7/2x-1/10y=1/1

$$\frac { 7 } { 2 x } - \frac { 1 } { 10 y } = \frac { 1 } { 1 }$$

Solve for y

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

$$x\neq 0\text{ and }x\neq \frac{7}{2}$$

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 10xy, the least common multiple of 2x,10y.

$$5y\times 7-x=10xy$$

Multiply 5 and 7 to get 35.

$$35y-x=10xy$$

Subtract 10xy from both sides.

$$35y-x-10xy=0$$

Add x to both sides. Anything plus zero gives itself.

$$35y-10xy=x$$

Combine all terms containing y.

$$\left(35-10x\right)y=x$$

Divide both sides by 35-10x.

$$\frac{\left(35-10x\right)y}{35-10x}=\frac{x}{35-10x}$$

Dividing by 35-10x undoes the multiplication by 35-10x.

$$y=\frac{x}{35-10x}$$

Divide x by 35-10x.

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

Variable y cannot be equal to 0.

$$y=\frac{x}{5\left(7-2x\right)}\text{, }y\neq 0$$

Solve for x

$$x=\frac{35y}{10y+1}$$

$$y\neq 0\text{ and }y\neq -\frac{1}{10}$$