Solve {l}{f(x)=2x-1}{8(x)=-3x+5}

$$\left. \begin{array} { l } { f ( x ) = 2 x - 1 } \\ { 8 ( x ) = - 3 x + 5 } \end{array} \right.$$

Solve for f, x

$$x=\frac{5}{11}\approx 0.454545455$$

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

Solution Steps

Consider the second equation. Add 3x to both sides.

$$8x+3x=5$$

Combine 8x and 3x to get 11x.

$$11x=5$$

Divide both sides by 11.

$$x=\frac{5}{11}$$

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

$$f\times \frac{5}{11}=2\times \frac{5}{11}-1$$

Multiply 2 and \frac{5}{11} to get \frac{10}{11}.

$$f\times \frac{5}{11}=\frac{10}{11}-1$$

Subtract 1 from \frac{10}{11} to get -\frac{1}{11}.

$$f\times \frac{5}{11}=-\frac{1}{11}$$

Multiply both sides by \frac{11}{5}, the reciprocal of \frac{5}{11}.

$$f=-\frac{1}{11}\times \frac{11}{5}$$

Multiply -\frac{1}{11} and \frac{11}{5} to get -\frac{1}{5}.

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

The system is now solved.

$$f=-\frac{1}{5} x=\frac{5}{11}$$