Solve {l}{4{(3m+2)}-5{(6m-1)}=2{(m-8)}-6{(7m-4)}}{n=4m}{o=n}{p=o}{q=p}{r=q}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{text{Solvefor}ytext{where}}{y=x}

$$\left. \begin{array} { l } { 4 {(3 m + 2)} - 5 {(6 m - 1)} = 2 {(m - 8)} - 6 {(7 m - 4)} }\\ { n = 4 m }\\ { o = n }\\ { p = o }\\ { q = p }\\ { r = q }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { \text{Solve for } y \text{ where} } \\ { y = x } \end{array} \right.$$

Solve for m, n, o, p, q, r, s, t, u, v, w, x, y

$$y=-\frac{10}{11}\approx -0.909090909$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4 by 3m+2.

$$12m+8-5\left(6m-1\right)=2\left(m-8\right)-6\left(7m-4\right)$$

Use the distributive property to multiply -5 by 6m-1.

$$12m+8-30m+5=2\left(m-8\right)-6\left(7m-4\right)$$

Combine 12m and -30m to get -18m.

$$-18m+8+5=2\left(m-8\right)-6\left(7m-4\right)$$

Add 8 and 5 to get 13.

$$-18m+13=2\left(m-8\right)-6\left(7m-4\right)$$

Use the distributive property to multiply 2 by m-8.

$$-18m+13=2m-16-6\left(7m-4\right)$$

Use the distributive property to multiply -6 by 7m-4.

$$-18m+13=2m-16-42m+24$$

Combine 2m and -42m to get -40m.

$$-18m+13=-40m-16+24$$

Add -16 and 24 to get 8.

$$-18m+13=-40m+8$$

Add 40m to both sides.

$$-18m+13+40m=8$$

Combine -18m and 40m to get 22m.

$$22m+13=8$$

Subtract 13 from both sides.

$$22m=8-13$$

Subtract 13 from 8 to get -5.

$$22m=-5$$

Divide both sides by 22.

$$m=-\frac{5}{22}$$

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

$$n=4\left(-\frac{5}{22}\right)$$

Multiply 4 and -\frac{5}{22} to get -\frac{10}{11}.

$$n=-\frac{10}{11}$$

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

$$o=-\frac{10}{11}$$

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

$$p=-\frac{10}{11}$$

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

$$q=-\frac{10}{11}$$

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

$$r=-\frac{10}{11}$$

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

$$s=-\frac{10}{11}$$

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

$$t=-\frac{10}{11}$$

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

$$u=-\frac{10}{11}$$

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

$$v=-\frac{10}{11}$$

Consider the equation (11). Insert the known values of variables into the equation.

$$w=-\frac{10}{11}$$

Consider the equation (12). Insert the known values of variables into the equation.

$$x=-\frac{10}{11}$$

Consider the equation (13). Insert the known values of variables into the equation.

$$y=-\frac{10}{11}$$

The system is now solved.

$$m=-\frac{5}{22} n=-\frac{10}{11} o=-\frac{10}{11} p=-\frac{10}{11} q=-\frac{10}{11} r=-\frac{10}{11} s=-\frac{10}{11} t=-\frac{10}{11} u=-\frac{10}{11} v=-\frac{10}{11} w=-\frac{10}{11} x=-\frac{10}{11} y=-\frac{10}{11}$$