Solve {l}{3x=30}{2y+x=20}{2u+y=13}{z=x+y*u}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 3 x = 30 }\\ { 2 y + x = 20 }\\ { 2 u + y = 13 }\\ { z = x + y \cdot u }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, u, z, a

$$a=30$$

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.

$$2u+5=13$$

Subtract 5 from both sides.

$$2u=13-5$$

Subtract 5 from 13 to get 8.

$$2u=8$$

Divide both sides by 2.

$$u=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$u=4$$

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

$$z=10+5\times 4$$

Multiply 5 and 4 to get 20.

$$z=10+20$$

Add 10 and 20 to get 30.

$$z=30$$

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

$$a=30$$

The system is now solved.

$$x=10 y=5 u=4 z=30 a=30$$