Solve {l}{x10^-10=3}{y=9*10^-10*10^13}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x 10 ^ {-10} = 3 }\\ { y = 9 \cdot 10 ^ {-10} \cdot 10 ^ {13} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=9000$$

Solution Steps

Consider the first equation. Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$x\times \frac{1}{10000000000}=3$$

Multiply both sides by 10000000000, the reciprocal of \frac{1}{10000000000}.

$$x=3\times 10000000000$$

Multiply 3 and 10000000000 to get 30000000000.

$$x=30000000000$$

Consider the second equation. To multiply powers of the same base, add their exponents. Add -10 and 13 to get 3.

$$y=9\times 10^{3}$$

Calculate 10 to the power of 3 and get 1000.

$$y=9\times 1000$$

Multiply 9 and 1000 to get 9000.

$$y=9000$$

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

$$z=9000$$

The system is now solved.

$$x=30000000000 y=9000 z=9000$$