Solve {l}{x=3}{y=6*sqrt{500}}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { x = 3 }\\ { y = 6 \cdot \sqrt{500} }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=60\sqrt{5}\approx 134.16407865$$

Solution Steps

Consider the second equation. Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$y=6\times 10\sqrt{5}$$

Multiply 6 and 10 to get 60.

$$y=60\sqrt{5}$$

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

$$z=60\sqrt{5}$$

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

$$a=60\sqrt{5}$$

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

$$b=60\sqrt{5}$$

The system is now solved.

$$x=3 y=60\sqrt{5} z=60\sqrt{5} a=60\sqrt{5} b=60\sqrt{5}$$