Solve {l}{4=6*7*10^-115*10^9*x/25}{y=13}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 4 = 6 \cdot 7 \cdot 10 ^ {-11} \frac{5 \cdot 10 ^ {9} \cdot x}{25} }\\ { y = 13 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=13$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 25.

$$100=6\times 7\times 10^{-11}\times 5\times 10^{9}x$$

To multiply powers of the same base, add their exponents. Add -11 and 9 to get -2.

$$100=6\times 7\times 10^{-2}\times 5x$$

Multiply 6 and 7 to get 42.

$$100=42\times 10^{-2}\times 5x$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$100=42\times \frac{1}{100}\times 5x$$

Multiply 42 and \frac{1}{100} to get \frac{21}{50}.

$$100=\frac{21}{50}\times 5x$$

Multiply \frac{21}{50} and 5 to get \frac{21}{10}.

$$100=\frac{21}{10}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{21}{10}x=100$$

Multiply both sides by \frac{10}{21}, the reciprocal of \frac{21}{10}.

$$x=100\times \frac{10}{21}$$

Multiply 100 and \frac{10}{21} to get \frac{1000}{21}.

$$x=\frac{1000}{21}$$

The system is now solved.

$$x=\frac{1000}{21} y=13 z=13$$