Solve (10-5+10^-4)x=(10^-3-10^-8)y

$$( 10 - 5 + 10 ^ { - 4 } ) x = ( 10 ^ { - 3 } - 10 ^ { - 8 } ) y$$

Solve for x

$$x=\frac{33333y}{166670000}$$

Steps for Solving Linear Equation

Subtract 5 from 10 to get 5.

$$\left(5+10^{-4}\right)x=\left(10^{-3}-10^{-8}\right)y$$

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

$$\left(5+\frac{1}{10000}\right)x=\left(10^{-3}-10^{-8}\right)y$$

Add 5 and \frac{1}{10000} to get \frac{50001}{10000}.

$$\frac{50001}{10000}x=\left(10^{-3}-10^{-8}\right)y$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{50001}{10000}x=\left(\frac{1}{1000}-10^{-8}\right)y$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\frac{50001}{10000}x=\left(\frac{1}{1000}-\frac{1}{100000000}\right)y$$

Subtract \frac{1}{100000000} from \frac{1}{1000} to get \frac{99999}{100000000}.

$$\frac{50001}{10000}x=\frac{99999}{100000000}y$$

The equation is in standard form.

$$\frac{50001}{10000}x=\frac{99999y}{100000000}$$

Divide both sides of the equation by \frac{50001}{10000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{50001}{10000}x}{\frac{50001}{10000}}=\frac{99999y}{\frac{50001}{10000}\times 100000000}$$

Dividing by \frac{50001}{10000} undoes the multiplication by \frac{50001}{10000}.

$$x=\frac{99999y}{\frac{50001}{10000}\times 100000000}$$

Divide \frac{99999y}{100000000} by \frac{50001}{10000} by multiplying \frac{99999y}{100000000} by the reciprocal of \frac{50001}{10000}.

$$x=\frac{33333y}{166670000}$$

Solve for y

$$y=\frac{166670000x}{33333}$$

Steps for Solving Linear Equation

Subtract 5 from 10 to get 5.

$$\left(5+10^{-4}\right)x=\left(10^{-3}-10^{-8}\right)y$$

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

$$\left(5+\frac{1}{10000}\right)x=\left(10^{-3}-10^{-8}\right)y$$

Add 5 and \frac{1}{10000} to get \frac{50001}{10000}.

$$\frac{50001}{10000}x=\left(10^{-3}-10^{-8}\right)y$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{50001}{10000}x=\left(\frac{1}{1000}-10^{-8}\right)y$$

Calculate 10 to the power of -8 and get \frac{1}{100000000}.

$$\frac{50001}{10000}x=\left(\frac{1}{1000}-\frac{1}{100000000}\right)y$$

Subtract \frac{1}{100000000} from \frac{1}{1000} to get \frac{99999}{100000000}.

$$\frac{50001}{10000}x=\frac{99999}{100000000}y$$

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

$$\frac{99999}{100000000}y=\frac{50001}{10000}x$$

The equation is in standard form.

$$\frac{99999}{100000000}y=\frac{50001x}{10000}$$

Divide both sides of the equation by \frac{99999}{100000000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{99999}{100000000}y}{\frac{99999}{100000000}}=\frac{50001x}{\frac{99999}{100000000}\times 10000}$$

Dividing by \frac{99999}{100000000} undoes the multiplication by \frac{99999}{100000000}.

$$y=\frac{50001x}{\frac{99999}{100000000}\times 10000}$$

Divide \frac{50001x}{10000} by \frac{99999}{100000000} by multiplying \frac{50001x}{10000} by the reciprocal of \frac{99999}{100000000}.

$$y=\frac{166670000x}{33333}$$