Solve {l}{3x=60}{x+2y=30}{y+2z=9}{x+a+z=42}{b=x+y*z}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 3 x = 60 }\\ { x + 2 y = 30 }\\ { y + 2 z = 9 }\\ { x + a + z = 42 }\\ { b = x + y \cdot z }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

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

$$c=30$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$x=\frac{60}{3}$$

Divide 60 by 3 to get 20.

$$x=20$$

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

$$20+2y=30$$

Subtract 20 from both sides.

$$2y=30-20$$

Subtract 20 from 30 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.

$$5+2z=9$$

Subtract 5 from both sides.

$$2z=9-5$$

Subtract 5 from 9 to get 4.

$$2z=4$$

Divide both sides by 2.

$$z=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$z=2$$

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

$$20+a+2=42$$

Add 20 and 2 to get 22.

$$22+a=42$$

Subtract 22 from both sides.

$$a=42-22$$

Subtract 22 from 42 to get 20.

$$a=20$$

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

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

Multiply 5 and 2 to get 10.

$$b=20+10$$

Add 20 and 10 to get 30.

$$b=30$$

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

$$c=30$$

The system is now solved.

$$x=20 y=5 z=2 a=20 b=30 c=30$$