Solve {l}{3x=30}{2y+x=20}{2u+y=3}{z=x+y+u}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 3 x = 30 }\\ { 2 y + x = 20 }\\ { 2 u + y = 3 }\\ { z = x + y + u }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, u, z, a

$$a=14$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$x=\frac{30}{3}$$

Divide 30 by 3 to get 10.

$$x=10$$

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

$$2y+10=20$$

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.

$$2u+5=3$$

Subtract 5 from both sides.

$$2u=3-5$$

Subtract 5 from 3 to get -2.

$$2u=-2$$

Divide both sides by 2.

$$u=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$u=-1$$

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

$$z=10+5-1$$

Add 10 and 5 to get 15.

$$z=15-1$$

Subtract 1 from 15 to get 14.

$$z=14$$

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

$$a=14$$

The system is now solved.

$$x=10 y=5 u=-1 z=14 a=14$$