Solve {l}{z_{1}+frac{v_{1}*v_{2}}{2}=z_{2}+frac{v_{2}}{2}}{v_{1}=3}{z_{1}=5}{z_{2}=10}

$$\left. \begin{array} { l } { z _ { 1 } + \frac { v _ { 1 } \cdot v _ { 2 } } { 2 } = z _ { 2 } + \frac { v _ { 2 } } { 2 } } \\ { v _ { 1 } = 3 } \\ { z _ { 1 } = 5 } \\ { z _ { 2 } = 10 } \end{array} \right.$$

Solve for z_1, v_1, v_2, z_2

$$z_{1}=5$$

$$v_{1}=3$$

$$v_{2}=5$$

$$z_{2}=10$$

Solution Steps

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

$$5+\frac{3v_{2}}{2}=10+\frac{v_{2}}{2}$$

Multiply both sides of the equation by 2.

$$10+3v_{2}=20+v_{2}$$

Subtract v_{2} from both sides.

$$10+3v_{2}-v_{2}=20$$

Combine 3v_{2} and -v_{2} to get 2v_{2}.

$$10+2v_{2}=20$$

Subtract 10 from both sides.

$$2v_{2}=20-10$$

Subtract 10 from 20 to get 10.

$$2v_{2}=10$$

Divide both sides by 2.

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

Divide 10 by 2 to get 5.

$$v_{2}=5$$

The system is now solved.

$$z_{1}=5 v_{1}=3 v_{2}=5 z_{2}=10$$