Solve {l}{5-6x=0}{y=3-5x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 - 6 x = 0 }\\ { y = 3 - 5 x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

Solution Steps

Consider the first equation. Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-5$$

Divide both sides by -6.

$$x=\frac{-5}{-6}$$

Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{6}$$

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

$$y=3-5\times \frac{5}{6}$$

Multiply -5 and \frac{5}{6} to get -\frac{25}{6}.

$$y=3-\frac{25}{6}$$

Subtract \frac{25}{6} from 3 to get -\frac{7}{6}.

$$y=-\frac{7}{6}$$

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

$$z=-\frac{7}{6}$$

The system is now solved.

$$x=\frac{5}{6} y=-\frac{7}{6} z=-\frac{7}{6}$$