Solve {l}{9x_{2}-7x_{3}=2}{-x_{3}=-2}{-3x_{1}+6x_{2}+8x_{3}=1}

$$\left. \begin{array}{l}{ 9 x _ { 2 } - 7 x _ { 3 } = 2 }\\{ - x _ { 3 } = - 2 }\\{ - 3 x _ { 1 } + 6 x _ { 2 } + 8 x _ { 3 } = 1 }\end{array} \right.$$

Solve for x_2, x_3, x_1

$$x_{2} = \frac{16}{9} = 1\frac{7}{9} \approx 1.777777778$$

$$x_{3}=2$$

$$x_{1} = \frac{77}{9} = 8\frac{5}{9} \approx 8.555555556$$

Solution Steps

Consider the second equation. Divide both sides by -1.

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$x_{3}=2$$

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

$$9x_{2}-7\times 2=2$$

Multiply -7 and 2 to get -14.

$$9x_{2}-14=2$$

Add 14 to both sides.

$$9x_{2}=2+14$$

Add 2 and 14 to get 16.

$$9x_{2}=16$$

Divide both sides by 9.

$$x_{2}=\frac{16}{9}$$

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

$$-3x_{1}+6\times \frac{16}{9}+8\times 2=1$$

Multiply 6 and \frac{16}{9} to get \frac{32}{3}.

$$-3x_{1}+\frac{32}{3}+8\times 2=1$$

Multiply 8 and 2 to get 16.

$$-3x_{1}+\frac{32}{3}+16=1$$

Add \frac{32}{3} and 16 to get \frac{80}{3}.

$$-3x_{1}+\frac{80}{3}=1$$

Subtract \frac{80}{3} from both sides.

$$-3x_{1}=1-\frac{80}{3}$$

Subtract \frac{80}{3} from 1 to get -\frac{77}{3}.

$$-3x_{1}=-\frac{77}{3}$$

Divide both sides by -3.

$$x_{1}=\frac{-\frac{77}{3}}{-3}$$

Express \frac{-\frac{77}{3}}{-3} as a single fraction.

$$x_{1}=\frac{-77}{3\left(-3\right)}$$

Multiply 3 and -3 to get -9.

$$x_{1}=\frac{-77}{-9}$$

Fraction \frac{-77}{-9} can be simplified to \frac{77}{9} by removing the negative sign from both the numerator and the denominator.

$$x_{1}=\frac{77}{9}$$

The system is now solved.

$$x_{2}=\frac{16}{9} x_{3}=2 x_{1}=\frac{77}{9}$$