Solve y/16=1/9y

$$\frac { y } { 16 } = \frac { 1 } { 9 y }$$

Solve for y

$$y = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$y = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps by Finding Square Root

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 144y, the least common multiple of 16,9y.

$$9yy=16$$

Multiply y and y to get y^{2}.

$$9y^{2}=16$$

Divide both sides by 9.

$$y^{2}=\frac{16}{9}$$

Take the square root of both sides of the equation.

$$y=\frac{4}{3} y=-\frac{4}{3}$$

Steps Using the Quadratic Formula

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 144y, the least common multiple of 16,9y.

$$9yy=16$$

Multiply y and y to get y^{2}.

$$9y^{2}=16$$

Subtract 16 from both sides.

$$9y^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 9\left(-16\right)}}{2\times 9}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 9\left(-16\right)}}{2\times 9}$$

Multiply -4 times 9.

$$y=\frac{0±\sqrt{-36\left(-16\right)}}{2\times 9}$$

Multiply -36 times -16.

$$y=\frac{0±\sqrt{576}}{2\times 9}$$

Take the square root of 576.

$$y=\frac{0±24}{2\times 9}$$

Multiply 2 times 9.

$$y=\frac{0±24}{18}$$

Now solve the equation y=\frac{0±24}{18} when ± is plus. Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

$$y=\frac{4}{3}$$

Now solve the equation y=\frac{0±24}{18} when ± is minus. Reduce the fraction \frac{-24}{18} to lowest terms by extracting and canceling out 6.

$$y=-\frac{4}{3}$$

The equation is now solved.

$$y=\frac{4}{3} y=-\frac{4}{3}$$