Solve {l}{-8r-3=-5r+9}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{y=x}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { -8 r - 3 = -5 r + 9 }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { y = x }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for r, s, t, u, v, w, x, y, z, a

$$a=-4$$

Solution Steps

Consider the first equation. Add 5r to both sides.

$$-8r-3+5r=9$$

Combine -8r and 5r to get -3r.

$$-3r-3=9$$

Add 3 to both sides.

$$-3r=9+3$$

Add 9 and 3 to get 12.

$$-3r=12$$

Divide both sides by -3.

$$r=\frac{12}{-3}$$

Divide 12 by -3 to get -4.

$$r=-4$$

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

$$s=-4$$

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

$$t=-4$$

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

$$u=-4$$

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

$$v=-4$$

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

$$w=-4$$

Consider the equation (7). Insert the known values of variables into the equation.

$$x=-4$$

Consider the equation (8). Insert the known values of variables into the equation.

$$y=-4$$

Consider the equation (9). Insert the known values of variables into the equation.

$$z=-4$$

Consider the equation (10). Insert the known values of variables into the equation.

$$a=-4$$

The system is now solved.

$$r=-4 s=-4 t=-4 u=-4 v=-4 w=-4 x=-4 y=-4 z=-4 a=-4$$