Solve {l}{-3x+1=0}{y=sqrt{2^6*3^4*5^2}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { -3 x + 1 = 0 }\\ { y = \sqrt{2 ^ {6} \cdot 3 ^ {4} \cdot 5 ^ {2}} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=360$$

Solution Steps

Consider the first equation. Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-3x=-1$$

Divide both sides by -3.

$$x=\frac{-1}{-3}$$

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{3}$$

Consider the second equation. Calculate 2 to the power of 6 and get 64.

$$y=\sqrt{64\times 3^{4}\times 5^{2}}$$

Calculate 3 to the power of 4 and get 81.

$$y=\sqrt{64\times 81\times 5^{2}}$$

Multiply 64 and 81 to get 5184.

$$y=\sqrt{5184\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$y=\sqrt{5184\times 25}$$

Multiply 5184 and 25 to get 129600.

$$y=\sqrt{129600}$$

Calculate the square root of 129600 and get 360.

$$y=360$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=360$$

The system is now solved.

$$x=\frac{1}{3} y=360 z=360$$