Solve sqrt{2y-3}=sqrt{5y-9}

$$\sqrt{ 2y-3 } = \sqrt{ 5y-9 }$$

Solve for y

$$y=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2y-3}\right)^{2}=\left(\sqrt{5y-9}\right)^{2}$$

Calculate \sqrt{2y-3} to the power of 2 and get 2y-3.

$$2y-3=\left(\sqrt{5y-9}\right)^{2}$$

Calculate \sqrt{5y-9} to the power of 2 and get 5y-9.

$$2y-3=5y-9$$

Subtract 5y from both sides.

$$2y-3-5y=-9$$

Combine 2y and -5y to get -3y.

$$-3y-3=-9$$

Add 3 to both sides.

$$-3y=-9+3$$

Add -9 and 3 to get -6.

$$-3y=-6$$

Divide both sides by -3.

$$y=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$y=2$$

Substitute 2 for y in the equation \sqrt{2y-3}=\sqrt{5y-9}.

$$\sqrt{2\times 2-3}=\sqrt{5\times 2-9}$$

Simplify. The value y=2 satisfies the equation.

$$1=1$$

Equation \sqrt{2y-3}=\sqrt{5y-9} has a unique solution.

$$y=2$$