Solve {l}{6-5x-3+2{(x)}=2}{y=6-5x{(-3-7x{(2)})}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 6 - 5 x - 3 + 2 {(x)} = 2 }\\ { y = 6 - 5 x {(-3 - 7 x {(2)})} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{169}{9} = 18\frac{7}{9} \approx 18.777777778$$

Solution Steps

Consider the first equation. Subtract 3 from 6 to get 3.

$$3-5x+2x=2$$

Combine -5x and 2x to get -3x.

$$3-3x=2$$

Subtract 3 from both sides.

$$-3x=2-3$$

Subtract 3 from 2 to get -1.

$$-3x=-1$$

Divide both sides by -3.

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

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

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

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

$$y=6-5\times \frac{1}{3}\left(-3-7\times \frac{1}{3}\times 2\right)$$

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

$$y=6-\frac{5}{3}\left(-3-7\times \frac{1}{3}\times 2\right)$$

Multiply 7 and \frac{1}{3} to get \frac{7}{3}.

$$y=6-\frac{5}{3}\left(-3-\frac{7}{3}\times 2\right)$$

Multiply \frac{7}{3} and 2 to get \frac{14}{3}.

$$y=6-\frac{5}{3}\left(-3-\frac{14}{3}\right)$$

Subtract \frac{14}{3} from -3 to get -\frac{23}{3}.

$$y=6-\frac{5}{3}\left(-\frac{23}{3}\right)$$

Multiply \frac{5}{3} and -\frac{23}{3} to get -\frac{115}{9}.

$$y=6-\left(-\frac{115}{9}\right)$$

The opposite of -\frac{115}{9} is \frac{115}{9}.

$$y=6+\frac{115}{9}$$

Add 6 and \frac{115}{9} to get \frac{169}{9}.

$$y=\frac{169}{9}$$

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

$$z=\frac{169}{9}$$

The system is now solved.

$$x=\frac{1}{3} y=\frac{169}{9} z=\frac{169}{9}$$