Solve {l}{2/3x_{1}+1/6*2=0}{4x_{1}+x_{2}=0}

$$\left. \begin{array} { l } { 2 / 3 x _ { 1 } + 1 / 6 \times 2 = 0 } \\ { 4 x _ { 1 } + x _ { 2 } = 0 } \end{array} \right.$$

Solve for x_1, x_2

$$x_{1}=-\frac{1}{2}=-0.5$$

$$x_{2}=2$$

Solution Steps

Consider the first equation. Multiply \frac{1}{6} and 2 to get \frac{1}{3}.

$$\frac{2}{3}x_{1}+\frac{1}{3}=0$$

Subtract \frac{1}{3} from both sides. Anything subtracted from zero gives its negation.

$$\frac{2}{3}x_{1}=-\frac{1}{3}$$

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$x_{1}=-\frac{1}{3}\times \frac{3}{2}$$

Multiply -\frac{1}{3} and \frac{3}{2} to get -\frac{1}{2}.

$$x_{1}=-\frac{1}{2}$$

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

$$4\left(-\frac{1}{2}\right)+x_{2}=0$$

Multiply 4 and -\frac{1}{2} to get -2.

$$-2+x_{2}=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$x_{2}=2$$

The system is now solved.

$$x_{1}=-\frac{1}{2} x_{2}=2$$