Solve {l}{a+b+c=-4}{a-b+c=-12}{9a+3b+c=2a}

$$\left\{ \begin{array} { l } { a + b + c = - 4 } \\ { a - b + c = - 12 } \\ { 9 a + 3 b + c = 2 a } \end{array} \right.$$

Solve for a, b, c

$$a=-\frac{2}{3}\approx -0.666666667$$

$$b=4$$

$$c = -\frac{22}{3} = -7\frac{1}{3} \approx -7.333333333$$

Short Steps Using Substitution

Solve a+b+c=-4 for a.

$$a=-b-c-4$$

Substitute -b-c-4 for a in the second and third equation.

$$-b-c-4-b+c=-12 9\left(-b-c-4\right)+3b+c=2\left(-b-c-4\right)$$

Solve these equations for b and c respectively.

$$b=4 c=-\frac{14}{3}-\frac{2}{3}b$$

Substitute 4 for b in the equation c=-\frac{14}{3}-\frac{2}{3}b.

$$c=-\frac{14}{3}-\frac{2}{3}\times 4$$

Calculate c from c=-\frac{14}{3}-\frac{2}{3}\times 4.

$$c=-\frac{22}{3}$$

Substitute 4 for b and -\frac{22}{3} for c in the equation a=-b-c-4.

$$a=-4-\left(-\frac{22}{3}\right)-4$$

Calculate a from a=-4-\left(-\frac{22}{3}\right)-4.

$$a=-\frac{2}{3}$$

The system is now solved.

$$a=-\frac{2}{3} b=4 c=-\frac{22}{3}$$