Solve sqrt{7y-1}=sqrt{9y-15}

$$\sqrt { 7 y - 1 } = \sqrt { 9 y - 15 }$$

Solve for y

$$y=7$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{7y-1}\right)^{2}=\left(\sqrt{9y-15}\right)^{2}$$

Calculate \sqrt{7y-1} to the power of 2 and get 7y-1.

$$7y-1=\left(\sqrt{9y-15}\right)^{2}$$

Calculate \sqrt{9y-15} to the power of 2 and get 9y-15.

$$7y-1=9y-15$$

Subtract 9y from both sides.

$$7y-1-9y=-15$$

Combine 7y and -9y to get -2y.

$$-2y-1=-15$$

Add 1 to both sides.

$$-2y=-15+1$$

Add -15 and 1 to get -14.

$$-2y=-14$$

Divide both sides by -2.

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

Divide -14 by -2 to get 7.

$$y=7$$

Substitute 7 for y in the equation \sqrt{7y-1}=\sqrt{9y-15}.

$$\sqrt{7\times 7-1}=\sqrt{9\times 7-15}$$

Simplify. The value y=7 satisfies the equation.

$$4\times 3^{\frac{1}{2}}=4\times 3^{\frac{1}{2}}$$

Equation \sqrt{7y-1}=\sqrt{9y-15} has a unique solution.

$$y=7$$