Solve {l}{8+2I_{1}-5.5=0}{11-7I_{1}-8I=0}

$$\left. \begin{array} { l } { 8 + 2 I _ { 1 } - 5.5 = 0 } \\ { 11 - 7 I _ { 1 } - 8 I = 0 } \end{array} \right.$$

Solve for I_1, I

$$I_{1}=-1.25$$

$$I=2.46875$$

Solution Steps

Consider the first equation. Subtract 5.5 from 8 to get 2.5.

$$2.5+2I_{1}=0$$

Subtract 2.5 from both sides. Anything subtracted from zero gives its negation.

$$2I_{1}=-2.5$$

Divide both sides by 2.

$$I_{1}=\frac{-2.5}{2}$$

Expand \frac{-2.5}{2} by multiplying both numerator and the denominator by 10.

$$I_{1}=\frac{-25}{20}$$

Reduce the fraction \frac{-25}{20} to lowest terms by extracting and canceling out 5.

$$I_{1}=-\frac{5}{4}$$

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

$$11-7\left(-\frac{5}{4}\right)-8I=0$$

Multiply -7 and -\frac{5}{4} to get \frac{35}{4}.

$$11+\frac{35}{4}-8I=0$$

Add 11 and \frac{35}{4} to get \frac{79}{4}.

$$\frac{79}{4}-8I=0$$

Subtract \frac{79}{4} from both sides. Anything subtracted from zero gives its negation.

$$-8I=-\frac{79}{4}$$

Divide both sides by -8.

$$I=\frac{-\frac{79}{4}}{-8}$$

Express \frac{-\frac{79}{4}}{-8} as a single fraction.

$$I=\frac{-79}{4\left(-8\right)}$$

Multiply 4 and -8 to get -32.

$$I=\frac{-79}{-32}$$

Fraction \frac{-79}{-32} can be simplified to \frac{79}{32} by removing the negative sign from both the numerator and the denominator.

$$I=\frac{79}{32}$$

The system is now solved.

$$I_{1}=-\frac{5}{4} I=\frac{79}{32}$$