Solve {l}{F(x)=2x-1}{9(x)=3x+9}

$$\left. \begin{array} { l } { F ( x ) = 2 x - 1 } \\ { 9 ( x ) = 3 x + 9 } \end{array} \right.$$

Solve for F, x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$F = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Solution Steps

Consider the second equation. Subtract 3x from both sides.

$$9x-3x=9$$

Combine 9x and -3x to get 6x.

$$6x=9$$

Divide both sides by 6.

$$x=\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{3}{2}$$

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

$$F\times \frac{3}{2}=2\times \frac{3}{2}-1$$

Multiply 2 and \frac{3}{2} to get 3.

$$F\times \frac{3}{2}=3-1$$

Subtract 1 from 3 to get 2.

$$F\times \frac{3}{2}=2$$

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.

$$F=2\times \frac{2}{3}$$

Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$F=\frac{4}{3}$$

The system is now solved.

$$F=\frac{4}{3} x=\frac{3}{2}$$