Solve {l}{x+y+z=800000}{1z=50000}{x-3z=0}{a=0}{b=0*5x+0*0*75y+0}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { x + y + z = 800000 }\\ { 1 z = 50000 }\\ { x - 3 z = 0 }\\ { a = 0 }\\ { b = 0 \cdot 5 x + 0 \cdot 0 \cdot 75 y + 0 }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$c=0$$

$$d=0$$

Solution Steps

Consider the second equation. Divide both sides by 1.

$$z=50000$$

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

$$x-3\times 50000=0$$

Multiply -3 and 50000 to get -150000.

$$x-150000=0$$

Add 150000 to both sides. Anything plus zero gives itself.

$$x=150000$$

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

$$150000+y+50000=800000$$

Add 150000 and 50000 to get 200000.

$$200000+y=800000$$

Subtract 200000 from both sides.

$$y=800000-200000$$

Subtract 200000 from 800000 to get 600000.

$$y=600000$$

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

$$b=0\times 5\times 150000+0\times 0\times 75\times 600000+0$$

Do the multiplications.

$$b=0\times 150000+0\times 75\times 600000+0$$

Multiply 0 and 150000 to get 0.

$$b=0+0\times 75\times 600000+0$$

Multiply 0 and 75 to get 0.

$$b=0+0\times 600000+0$$

Multiply 0 and 600000 to get 0.

$$b=0+0+0$$

Add 0 and 0 to get 0.

$$b=0$$

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

$$d=0$$

The system is now solved.

$$x=150000 y=600000 z=50000 a=0 b=0 c=0 d=0$$