Solve {l}{F(x)=3x+2}{text{og}(x)=6x-4}

$$\left. \begin{array} { l } { F ( x ) = 3 x + 2 } \\ { \text { og } ( x ) = 6 x - 4 } \end{array} \right.$$

Solve for F, x

$$x=\frac{4}{5}=0.8$$

$$F = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Solution Steps

Consider the second equation. Subtract 6x from both sides.

$$x-6x=-4$$

Combine x and -6x to get -5x.

$$-5x=-4$$

Divide both sides by -5.

$$x=\frac{-4}{-5}$$

Fraction \frac{-4}{-5} can be simplified to \frac{4}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{5}$$

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

$$F\times \frac{4}{5}=3\times \frac{4}{5}+2$$

Multiply 3 and \frac{4}{5} to get \frac{12}{5}.

$$F\times \frac{4}{5}=\frac{12}{5}+2$$

Add \frac{12}{5} and 2 to get \frac{22}{5}.

$$F\times \frac{4}{5}=\frac{22}{5}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.

$$F=\frac{22}{5}\times \frac{5}{4}$$

Multiply \frac{22}{5} and \frac{5}{4} to get \frac{11}{2}.

$$F=\frac{11}{2}$$

The system is now solved.

$$F=\frac{11}{2} x=\frac{4}{5}$$