Solve {c}{f=-av}{f=10}{v=50}

$$\left. \begin{array} { c } { f = - a v } \\ { f = 10 } \\ { v = 50 } \end{array} \right.$$

Solve for f, a, v

$$f=10$$

$$a=-\frac{1}{5}=-0.2$$

$$v=50$$

Solution Steps

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

$$10=\left(-a\right)\times 50$$

Divide both sides by 50.

$$\frac{10}{50}=-a$$

Reduce the fraction \frac{10}{50} to lowest terms by extracting and canceling out 10.

$$\frac{1}{5}=-a$$

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

$$-a=\frac{1}{5}$$

Divide both sides by -1.

$$a=\frac{\frac{1}{5}}{-1}$$

Express \frac{\frac{1}{5}}{-1} as a single fraction.

$$a=\frac{1}{5\left(-1\right)}$$

Multiply 5 and -1 to get -5.

$$a=\frac{1}{-5}$$

Fraction \frac{1}{-5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$a=-\frac{1}{5}$$

The system is now solved.

$$f=10 a=-\frac{1}{5} v=50$$