Solve {l}{x=20*60*20*10*2*8*4*27/60*20*10*8*1*9*3}{y=x*60*20*10*8*1*9*3}{z=27*20*60*20*10*2*8*4}{text{Solvefor}a,btext{where}}{a=y}{b=z}

$$\left. \begin{array} { l } { x = \frac{20 \cdot 60 \cdot 20 \cdot 10 \cdot 2 \cdot 8 \cdot 4 \cdot 27}{60 \cdot 20 \cdot 10 \cdot 8 \cdot 1 \cdot 9 \cdot 3} }\\ { y = x \cdot 60 \cdot 20 \cdot 10 \cdot 8 \cdot 1 \cdot 9 \cdot 3 }\\ { z = 27 \cdot 20 \cdot 60 \cdot 20 \cdot 10 \cdot 2 \cdot 8 \cdot 4 }\\ { \text{Solve for } a,b \text{ where} } \\ { a = y }\\ { b = z } \end{array} \right.$$

Solve for x, y, z, a, b

$$a=414720000$$

$$b=414720000$$

Solution Steps

Consider the first equation. Cancel out 2\times 2\times 2\times 3\times 3\times 9\times 10\times 20\times 20 in both numerator and denominator.

$$x=4\times 5\times 8$$

Multiply 4 and 5 to get 20.

$$x=20\times 8$$

Multiply 20 and 8 to get 160.

$$x=160$$

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

$$y=160\times 60\times 20\times 10\times 8\times 1\times 9\times 3$$

Multiply 160 and 60 to get 9600.

$$y=9600\times 20\times 10\times 8\times 1\times 9\times 3$$

Multiply 9600 and 20 to get 192000.

$$y=192000\times 10\times 8\times 1\times 9\times 3$$

Multiply 192000 and 10 to get 1920000.

$$y=1920000\times 8\times 1\times 9\times 3$$

Multiply 1920000 and 8 to get 15360000.

$$y=15360000\times 1\times 9\times 3$$

Multiply 15360000 and 1 to get 15360000.

$$y=15360000\times 9\times 3$$

Multiply 15360000 and 9 to get 138240000.

$$y=138240000\times 3$$

Multiply 138240000 and 3 to get 414720000.

$$y=414720000$$

Consider the third equation. Multiply 27 and 20 to get 540.

$$z=540\times 60\times 20\times 10\times 2\times 8\times 4$$

Multiply 540 and 60 to get 32400.

$$z=32400\times 20\times 10\times 2\times 8\times 4$$

Multiply 32400 and 20 to get 648000.

$$z=648000\times 10\times 2\times 8\times 4$$

Multiply 648000 and 10 to get 6480000.

$$z=6480000\times 2\times 8\times 4$$

Multiply 6480000 and 2 to get 12960000.

$$z=12960000\times 8\times 4$$

Multiply 12960000 and 8 to get 103680000.

$$z=103680000\times 4$$

Multiply 103680000 and 4 to get 414720000.

$$z=414720000$$

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

$$a=414720000$$

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

$$b=414720000$$

The system is now solved.

$$x=160 y=414720000 z=414720000 a=414720000 b=414720000$$