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

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

Solve for z_1, v_1, z_2, V_2

$$z_{1}=5$$

$$v_{1}=3$$

$$z_{2}=10$$

$$V_{2}=-7$$

Solution Steps

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

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

Multiply both sides of the equation by 2.

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

Add 10 and 3 to get 13.

$$13=20+V_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$20+V_{2}=13$$

Subtract 20 from both sides.

$$V_{2}=13-20$$

Subtract 20 from 13 to get -7.

$$V_{2}=-7$$

The system is now solved.

$$z_{1}=5 v_{1}=3 z_{2}=10 V_{2}=-7$$