Solve {l}{67*10^-11*200x=1*4*10^-4*{(9+0*0*10^3)}^2}{y=6}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 67 \cdot 10 ^ {-11} \cdot 200 x = 1 \cdot 4 \cdot 10 ^ {-4} \cdot {(9 + 0 \cdot 0 \cdot 10 ^ {3})} ^ {2} }\\ { y = 6 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=6$$

Solution Steps

Consider the first equation. Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$67\times \frac{1}{100000000000}\times 200x=1\times 4\times 10^{-4}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Multiply 67 and \frac{1}{100000000000} to get \frac{67}{100000000000}.

$$\frac{67}{100000000000}\times 200x=1\times 4\times 10^{-4}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Multiply \frac{67}{100000000000} and 200 to get \frac{67}{500000000}.

$$\frac{67}{500000000}x=1\times 4\times 10^{-4}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Multiply 1 and 4 to get 4.

$$\frac{67}{500000000}x=4\times 10^{-4}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{67}{500000000}x=4\times \frac{1}{10000}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Multiply 4 and \frac{1}{10000} to get \frac{1}{2500}.

$$\frac{67}{500000000}x=\frac{1}{2500}\left(9+0\times 0\times 10^{3}\right)^{2}$$

Multiply 0 and 0 to get 0.

$$\frac{67}{500000000}x=\frac{1}{2500}\left(9+0\times 10^{3}\right)^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{67}{500000000}x=\frac{1}{2500}\left(9+0\times 1000\right)^{2}$$

Multiply 0 and 1000 to get 0.

$$\frac{67}{500000000}x=\frac{1}{2500}\left(9+0\right)^{2}$$

Add 9 and 0 to get 9.

$$\frac{67}{500000000}x=\frac{1}{2500}\times 9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{67}{500000000}x=\frac{1}{2500}\times 81$$

Multiply \frac{1}{2500} and 81 to get \frac{81}{2500}.

$$\frac{67}{500000000}x=\frac{81}{2500}$$

Multiply both sides by \frac{500000000}{67}, the reciprocal of \frac{67}{500000000}.

$$x=\frac{81}{2500}\times \frac{500000000}{67}$$

Multiply \frac{81}{2500} and \frac{500000000}{67} to get \frac{16200000}{67}.

$$x=\frac{16200000}{67}$$

The system is now solved.

$$x=\frac{16200000}{67} y=6 z=6$$