Solve {l}{9{(x)}=3}{y=-5x-24}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 9 {(x)} = 3 }\\ { y = -5 x - 24 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for x, y, z, a, b, c

$$c = -\frac{77}{3} = -25\frac{2}{3} \approx -25.666666667$$

Solution Steps

Consider the first equation. Divide both sides by 9.

$$x=\frac{3}{9}$$

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

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

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

$$y=-5\times \frac{1}{3}-24$$

Multiply -5 and \frac{1}{3} to get -\frac{5}{3}.

$$y=-\frac{5}{3}-24$$

Subtract 24 from -\frac{5}{3} to get -\frac{77}{3}.

$$y=-\frac{77}{3}$$

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

$$z=-\frac{77}{3}$$

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

$$a=-\frac{77}{3}$$

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

$$b=-\frac{77}{3}$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=-\frac{77}{3}$$

The system is now solved.

$$x=\frac{1}{3} y=-\frac{77}{3} z=-\frac{77}{3} a=-\frac{77}{3} b=-\frac{77}{3} c=-\frac{77}{3}$$