Solve {l}{f=14*0.6/1.3}{F=f*50*(120-2*13)}

$$\left. \begin{array} { l } { f = 14 \times \frac { 0.6 } { 1.3 } } \\ { F = f \times 50 \times ( 120 - 2 \times 13 ) } \end{array} \right.$$

Solve for f, F

$$f = \frac{84}{13} = 6\frac{6}{13} \approx 6.461538462$$

$$F = \frac{394800}{13} = 30369\frac{3}{13} \approx 30369.230769231$$

Solution Steps

Consider the first equation. Expand \frac{0.6}{1.3} by multiplying both numerator and the denominator by 10.

$$f=14\times \frac{6}{13}$$

Multiply 14 and \frac{6}{13} to get \frac{84}{13}.

$$f=\frac{84}{13}$$

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

$$F=\frac{84}{13}\times 50\left(120-2\times 13\right)$$

Multiply \frac{84}{13} and 50 to get \frac{4200}{13}.

$$F=\frac{4200}{13}\left(120-2\times 13\right)$$

Multiply 2 and 13 to get 26.

$$F=\frac{4200}{13}\left(120-26\right)$$

Subtract 26 from 120 to get 94.

$$F=\frac{4200}{13}\times 94$$

Multiply \frac{4200}{13} and 94 to get \frac{394800}{13}.

$$F=\frac{394800}{13}$$

The system is now solved.

$$f=\frac{84}{13} F=\frac{394800}{13}$$