Solve {l}{3-3y=-4}{z=-2y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 3 - 3 y = -4 }\\ { z = -2 y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for y, z, a, b, c

$$c = -\frac{14}{3} = -4\frac{2}{3} \approx -4.666666667$$

Solution Steps

Consider the first equation. Subtract 3 from both sides.

$$-3y=-4-3$$

Subtract 3 from -4 to get -7.

$$-3y=-7$$

Divide both sides by -3.

$$y=\frac{-7}{-3}$$

Fraction \frac{-7}{-3} can be simplified to \frac{7}{3} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{7}{3}$$

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

$$z=-2\times \frac{7}{3}$$

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

$$z=-\frac{14}{3}$$

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

$$a=-\frac{14}{3}$$

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

$$b=-\frac{14}{3}$$

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

$$c=-\frac{14}{3}$$

The system is now solved.

$$y=\frac{7}{3} z=-\frac{14}{3} a=-\frac{14}{3} b=-\frac{14}{3} c=-\frac{14}{3}$$