Solve f(x)=4x-6,9(x)=x+3

$$f ( x ) = 4 x - 6,9 ( x ) = x + 3$$

Solve for f, x

$$x=\frac{3}{8}=0.375$$

$$f=-12$$

Solution Steps

Consider the second equation. Subtract x from both sides.

$$9x-x=3$$

Combine 9x and -x to get 8x.

$$8x=3$$

Divide both sides by 8.

$$x=\frac{3}{8}$$

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

$$f\times \frac{3}{8}=4\times \frac{3}{8}-6$$

Multiply 4 and \frac{3}{8} to get \frac{3}{2}.

$$f\times \frac{3}{8}=\frac{3}{2}-6$$

Subtract 6 from \frac{3}{2} to get -\frac{9}{2}.

$$f\times \frac{3}{8}=-\frac{9}{2}$$

Multiply both sides by \frac{8}{3}, the reciprocal of \frac{3}{8}.

$$f=-\frac{9}{2}\times \frac{8}{3}$$

Multiply -\frac{9}{2} and \frac{8}{3} to get -12.

$$f=-12$$

The system is now solved.

$$f=-12 x=\frac{3}{8}$$