Solve {l}{50{(x/2)}=795}{y=5{(x)}+2{(3x)}+2x+0}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 50 {(\frac{x}{2})} = 795 }\\ { y = 5 {(x)} + 2 {(3 x)} + 2 x + 0 }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

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

$$c = \frac{2067}{5} = 413\frac{2}{5} = 413.4$$

Solution Steps

Consider the first equation. Divide both sides by 50.

$$\frac{x}{2}=\frac{795}{50}$$

Reduce the fraction \frac{795}{50} to lowest terms by extracting and canceling out 5.

$$\frac{x}{2}=\frac{159}{10}$$

Multiply both sides by 2.

$$x=\frac{159}{10}\times 2$$

Multiply \frac{159}{10} and 2 to get \frac{159}{5}.

$$x=\frac{159}{5}$$

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

$$y=5\times \frac{159}{5}+2\times 3\times \frac{159}{5}+2\times \frac{159}{5}+0$$

Multiply 5 and \frac{159}{5} to get 159.

$$y=159+2\times 3\times \frac{159}{5}+2\times \frac{159}{5}+0$$

Multiply 2 and 3 to get 6.

$$y=159+6\times \frac{159}{5}+2\times \frac{159}{5}+0$$

Multiply 6 and \frac{159}{5} to get \frac{954}{5}.

$$y=159+\frac{954}{5}+2\times \frac{159}{5}+0$$

Add 159 and \frac{954}{5} to get \frac{1749}{5}.

$$y=\frac{1749}{5}+2\times \frac{159}{5}+0$$

Multiply 2 and \frac{159}{5} to get \frac{318}{5}.

$$y=\frac{1749}{5}+\frac{318}{5}+0$$

Add \frac{1749}{5} and \frac{318}{5} to get \frac{2067}{5}.

$$y=\frac{2067}{5}+0$$

Add \frac{2067}{5} and 0 to get \frac{2067}{5}.

$$y=\frac{2067}{5}$$

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

$$z=\frac{2067}{5}$$

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

$$a=\frac{2067}{5}$$

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

$$b=\frac{2067}{5}$$

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

$$c=\frac{2067}{5}$$

The system is now solved.

$$x=\frac{159}{5} y=\frac{2067}{5} z=\frac{2067}{5} a=\frac{2067}{5} b=\frac{2067}{5} c=\frac{2067}{5}$$