Solve {l}{36/126=n/112}{o=1*2}{p=o}{q=p}{r=q}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{text{Solvefor}ytext{where}}{y=x}

$$\left. \begin{array} { l } { \frac{36}{126} = n / 112 }\\ { o = 1 \cdot 2 }\\ { p = o }\\ { q = p }\\ { r = q }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { \text{Solve for } y \text{ where} } \\ { y = x } \end{array} \right.$$

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

$$y=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 1008, the least common multiple of 126,112.

$$8\times 36=9n$$

Multiply 8 and 36 to get 288.

$$288=9n$$

Swap sides so that all variable terms are on the left hand side.

$$9n=288$$

Divide both sides by 9.

$$n=\frac{288}{9}$$

Divide 288 by 9 to get 32.

$$n=32$$

Consider the second equation. Multiply 1 and 2 to get 2.

$$o=2$$

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

$$p=2$$

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

$$q=2$$

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

$$r=2$$

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

$$s=2$$

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

$$t=2$$

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

$$u=2$$

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

$$v=2$$

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

$$w=2$$

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

$$x=2$$

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

$$y=2$$

The system is now solved.

$$n=32 o=2 p=2 q=2 r=2 s=2 t=2 u=2 v=2 w=2 x=2 y=2$$