Solve 1/3x+1/7y^2=17

$$\frac { 1 } { 3 x } + \frac { 1 } { 7 } y ^ { 2 } = 17$$

Solve for x (complex solution)

$$x=-\frac{7}{3\left(y^{2}-119\right)}$$

$$y\neq -\sqrt{119}\text{ and }y\neq \sqrt{119}$$

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 21x, the least common multiple of 3x,7.

$$7+\frac{1}{7}y^{2}\times 21x=357x$$

Multiply \frac{1}{7} and 21 to get 3.

$$7+3y^{2}x=357x$$

Subtract 357x from both sides.

$$7+3y^{2}x-357x=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$3y^{2}x-357x=-7$$

Combine all terms containing x.

$$\left(3y^{2}-357\right)x=-7$$

Divide both sides by 3y^{2}-357.

$$\frac{\left(3y^{2}-357\right)x}{3y^{2}-357}=-\frac{7}{3y^{2}-357}$$

Dividing by 3y^{2}-357 undoes the multiplication by 3y^{2}-357.

$$x=-\frac{7}{3y^{2}-357}$$

Divide -7 by 3y^{2}-357.

$$x=-\frac{7}{3\left(y^{2}-119\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{7}{3\left(y^{2}-119\right)}\text{, }x\neq 0$$

Solve for x

$$x=-\frac{7}{3\left(y^{2}-119\right)}$$

$$|y|\neq \sqrt{119}$$

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 21x, the least common multiple of 3x,7.

$$7+\frac{1}{7}y^{2}\times 21x=357x$$

Multiply \frac{1}{7} and 21 to get 3.

$$7+3y^{2}x=357x$$

Subtract 357x from both sides.

$$7+3y^{2}x-357x=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$3y^{2}x-357x=-7$$

Combine all terms containing x.

$$\left(3y^{2}-357\right)x=-7$$

Divide both sides by 3y^{2}-357.

$$\frac{\left(3y^{2}-357\right)x}{3y^{2}-357}=-\frac{7}{3y^{2}-357}$$

Dividing by 3y^{2}-357 undoes the multiplication by 3y^{2}-357.

$$x=-\frac{7}{3y^{2}-357}$$

Divide -7 by 3y^{2}-357.

$$x=-\frac{7}{3\left(y^{2}-119\right)}$$

Variable x cannot be equal to 0.

$$x=-\frac{7}{3\left(y^{2}-119\right)}\text{, }x\neq 0$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{1071-\frac{21}{x}}}{3}$$

$$y=\frac{\sqrt{1071-\frac{21}{x}}}{3}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{1071-\frac{21}{x}}}{3}$$

$$y=-\frac{\sqrt{1071-\frac{21}{x}}}{3}\text{, }x<0\text{ or }x\geq \frac{1}{51}$$