Solve {l}{6x=30}{2x+2y=20}{6z+y=17}{a=x+4z+y}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { 6 x = 30 }\\ { 2 x + 2 y = 20 }\\ { 6 z + y = 17 }\\ { a = x + 4 z + y }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

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

$$d=18$$

Solution Steps

Consider the first equation. Divide both sides by 6.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$

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

$$2\times 5+2y=20$$

Multiply 2 and 5 to get 10.

$$10+2y=20$$

Subtract 10 from both sides.

$$2y=20-10$$

Subtract 10 from 20 to get 10.

$$2y=10$$

Divide both sides by 2.

$$y=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$y=5$$

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

$$6z+5=17$$

Subtract 5 from both sides.

$$6z=17-5$$

Subtract 5 from 17 to get 12.

$$6z=12$$

Divide both sides by 6.

$$z=\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$z=2$$

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

$$a=5+4\times 2+5$$

Multiply 4 and 2 to get 8.

$$a=5+8+5$$

Add 5 and 8 to get 13.

$$a=13+5$$

Add 13 and 5 to get 18.

$$a=18$$

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

$$b=18$$

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

$$c=18$$

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

$$d=18$$

The system is now solved.

$$x=5 y=5 z=2 a=18 b=18 c=18 d=18$$