Solve {l}{-6+57*4quadI_{2}-28*2I_{1}=0}{24+35*2I_{1}+29*2I_{1}=0}

$$\left. \begin{array} { l } { - 6 + 57 \cdot 4 \quad I _ { 2 } - 28 \cdot 2 I _ { 1 } = 0 } \\ { 24 + 35 \cdot 2 I _ { 1 } + 29 \cdot 2 I _ { 1 } = 0 } \end{array} \right.$$

Solve for I_2, I_1

$$I_{2}=-\frac{3}{152}\approx -0.019736842$$

$$I_{1}=-\frac{3}{16}=-0.1875$$

Solution Steps

Consider the second equation. Do the multiplications.

$$24+70I_{1}+58I_{1}=0$$

Combine 70I_{1} and 58I_{1} to get 128I_{1}.

$$24+128I_{1}=0$$

Subtract 24 from both sides. Anything subtracted from zero gives its negation.

$$128I_{1}=-24$$

Divide both sides by 128.

$$I_{1}=\frac{-24}{128}$$

Reduce the fraction \frac{-24}{128} to lowest terms by extracting and canceling out 8.

$$I_{1}=-\frac{3}{16}$$

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

$$-6+57\times 4I_{2}-28\times 2\left(-\frac{3}{16}\right)=0$$

Multiply 57 and 4 to get 228.

$$-6+228I_{2}-28\times 2\left(-\frac{3}{16}\right)=0$$

Multiply 28 and 2 to get 56.

$$-6+228I_{2}-56\left(-\frac{3}{16}\right)=0$$

Multiply 56 and -\frac{3}{16} to get -\frac{21}{2}.

$$-6+228I_{2}-\left(-\frac{21}{2}\right)=0$$

The opposite of -\frac{21}{2} is \frac{21}{2}.

$$-6+228I_{2}+\frac{21}{2}=0$$

Add -6 and \frac{21}{2} to get \frac{9}{2}.

$$\frac{9}{2}+228I_{2}=0$$

Subtract \frac{9}{2} from both sides. Anything subtracted from zero gives its negation.

$$228I_{2}=-\frac{9}{2}$$

Divide both sides by 228.

$$I_{2}=\frac{-\frac{9}{2}}{228}$$

Express \frac{-\frac{9}{2}}{228} as a single fraction.

$$I_{2}=\frac{-9}{2\times 228}$$

Multiply 2 and 228 to get 456.

$$I_{2}=\frac{-9}{456}$$

Reduce the fraction \frac{-9}{456} to lowest terms by extracting and canceling out 3.

$$I_{2}=-\frac{3}{152}$$

The system is now solved.

$$I_{2}=-\frac{3}{152} I_{1}=-\frac{3}{16}$$