Solve {l}{3x+8x+2x+x=24}{y=13x}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 3 x + 8 x + 2 x + x = 24 }\\ { y = 13 x }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z, a

$$a = \frac{156}{7} = 22\frac{2}{7} \approx 22.285714286$$

Solution Steps

Consider the first equation. Combine 3x and 8x to get 11x.

$$11x+2x+x=24$$

Combine 11x and 2x to get 13x.

$$13x+x=24$$

Combine 13x and x to get 14x.

$$14x=24$$

Divide both sides by 14.

$$x=\frac{24}{14}$$

Reduce the fraction \frac{24}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{12}{7}$$

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

$$y=13\times \frac{12}{7}$$

Multiply 13 and \frac{12}{7} to get \frac{156}{7}.

$$y=\frac{156}{7}$$

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

$$z=\frac{156}{7}$$

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

$$a=\frac{156}{7}$$

The system is now solved.

$$x=\frac{12}{7} y=\frac{156}{7} z=\frac{156}{7} a=\frac{156}{7}$$