Solve 1/y+3/2x=7

$$\frac { 1 } { y } + \frac { 3 } { 2 x } = 7$$

Solve for x

$$x=-\frac{3y}{2\left(1-7y\right)}$$

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

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

$$2x+y\times 3=14xy$$

Subtract 14xy from both sides.

$$2x+y\times 3-14xy=0$$

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

$$2x-14xy=-y\times 3$$

Multiply -1 and 3 to get -3.

$$2x-14xy=-3y$$

Combine all terms containing x.

$$\left(2-14y\right)x=-3y$$

Divide both sides by -14y+2.

$$\frac{\left(2-14y\right)x}{2-14y}=-\frac{3y}{2-14y}$$

Dividing by -14y+2 undoes the multiplication by -14y+2.

$$x=-\frac{3y}{2-14y}$$

Divide -3y by -14y+2.

$$x=-\frac{3y}{2\left(1-7y\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{3y}{2\left(1-7y\right)}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2x}{3-14x}$$

$$x\neq 0\text{ and }x\neq \frac{3}{14}$$

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

$$2x+y\times 3=14xy$$

Subtract 14xy from both sides.

$$2x+y\times 3-14xy=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$y\times 3-14xy=-2x$$

Combine all terms containing y.

$$\left(3-14x\right)y=-2x$$

Divide both sides by 3-14x.

$$\frac{\left(3-14x\right)y}{3-14x}=-\frac{2x}{3-14x}$$

Dividing by 3-14x undoes the multiplication by 3-14x.

$$y=-\frac{2x}{3-14x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2x}{3-14x}\text{, }y\neq 0$$