Solve {c}{1/10U_{1}+(U_{1}-U_{2})*1/2=2+5I_{x}}{(U_{2}-U_{1})*1/2+1/4U_{2}+5I_{x}=0}{frac{U_{1}}{10}=I_{x}}

$$\left. \begin{array} { c } { \frac { 1 } { 10 } U _ { 1 } + ( U _ { 1 } - U _ { 2 } ) \times \frac { 1 } { 2 } = 2 + 5 I _ { x } } \\ { ( U _ { 2 } - U _ { 1 } ) \times \frac { 1 } { 2 } + \frac { 1 } { 4 } U _ { 2 } + 5 I _ { x } = 0 } \\ { \frac { U _ { 1 } } { 10 } = I _ { x } } \end{array} \right.$$

Solve for U_1, U_2, I_x

$$U_{1}=20$$

$$U_{2}=0$$

$$I_{x}=2$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$6U_{1}-5U_{2}=20+50I_{x} 3U_{2}-2U_{1}+20I_{x}=0 U_{1}=10I_{x}$$

Reorder the equations.

$$U_{1}=10I_{x} 3U_{2}-2U_{1}+20I_{x}=0 6U_{1}-5U_{2}=20+50I_{x}$$

Substitute 10I_{x} for U_{1} in the second and third equation.

$$3U_{2}-2\times 10I_{x}+20I_{x}=0 6\times 10I_{x}-5U_{2}=20+50I_{x}$$

Solve these equations for U_{2} and I_{x} respectively.

$$U_{2}=0 I_{x}=2+\frac{1}{2}U_{2}$$

Substitute 0 for U_{2} in the equation I_{x}=2+\frac{1}{2}U_{2}.

$$I_{x}=2+\frac{1}{2}\times 0$$

Calculate I_{x} from I_{x}=2+\frac{1}{2}\times 0.

$$I_{x}=2$$

Substitute 2 for I_{x} in the equation U_{1}=10I_{x}.

$$U_{1}=10\times 2$$

Calculate U_{1} from U_{1}=10\times 2.

$$U_{1}=20$$

The system is now solved.

$$U_{1}=20 U_{2}=0 I_{x}=2$$