Solve {l}{0.84=0.992x}{0.16=y+0.008x}

$$\left. \begin{array} { l } { 0.84 = 0.992 x } \\ { 0.16 = y + 0.008 x } \end{array} \right.$$

Solve for x, y

$$x=\frac{105}{124}\approx 0.846774194$$

$$y=\frac{19}{124}\approx 0.153225806$$

Solution Steps

Consider the first equation. Divide both sides by 0.992.

$$\frac{0.84}{0.992}=x$$

Expand \frac{0.84}{0.992} by multiplying both numerator and the denominator by 1000.

$$\frac{840}{992}=x$$

Reduce the fraction \frac{840}{992} to lowest terms by extracting and canceling out 8.

$$\frac{105}{124}=x$$

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

$$x=\frac{105}{124}$$

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

$$0.16=y+0.008\times \frac{105}{124}$$

Multiply 0.008 and \frac{105}{124} to get \frac{21}{3100}.

$$0.16=y+\frac{21}{3100}$$

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

$$y+\frac{21}{3100}=0.16$$

Subtract \frac{21}{3100} from both sides.

$$y=0.16-\frac{21}{3100}$$

Subtract \frac{21}{3100} from 0.16 to get \frac{19}{124}.

$$y=\frac{19}{124}$$

The system is now solved.

$$x=\frac{105}{124} y=\frac{19}{124}$$