Solve {l}{x+y=10}{y+z=20}{x+2=24}{a=x+y+z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { x + y = 10 }\\ { y + z = 20 }\\ { x + 2 = 24 }\\ { a = x + y + z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=42$$

Solution Steps

Consider the third equation. Subtract 2 from both sides.

$$x=24-2$$

Subtract 2 from 24 to get 22.

$$x=22$$

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

$$22+y=10$$

Subtract 22 from both sides.

$$y=10-22$$

Subtract 22 from 10 to get -12.

$$y=-12$$

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

$$-12+z=20$$

Add 12 to both sides.

$$z=20+12$$

Add 20 and 12 to get 32.

$$z=32$$

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

$$a=22-12+32$$

Subtract 12 from 22 to get 10.

$$a=10+32$$

Add 10 and 32 to get 42.

$$a=42$$

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

$$b=42$$

The system is now solved.

$$x=22 y=-12 z=32 a=42 b=42$$