Solve {c}{a+b+c=-7}{4a-2b+c=5}{9a+3b+c=-5}

$$\left\{ \begin{array} { c } { a + b + c = - 7 } \\ { 4 a - 2 b + c = 5 } \\ { 9 a + 3 b + c = - 5 } \end{array} \right.$$

Solve for a, b, c

$$a=1$$

$$b=-3$$

$$c=-5$$

Short Steps Using Substitution

Solve a+b+c=-7 for a.

$$a=-b-c-7$$

Substitute -b-c-7 for a in the second and third equation.

$$4\left(-b-c-7\right)-2b+c=5 9\left(-b-c-7\right)+3b+c=-5$$

Solve these equations for b and c respectively.

$$b=-\frac{11}{2}-\frac{1}{2}c c=-\frac{29}{4}-\frac{3}{4}b$$

Substitute -\frac{11}{2}-\frac{1}{2}c for b in the equation c=-\frac{29}{4}-\frac{3}{4}b.

$$c=-\frac{29}{4}-\frac{3}{4}\left(-\frac{11}{2}-\frac{1}{2}c\right)$$

Solve c=-\frac{29}{4}-\frac{3}{4}\left(-\frac{11}{2}-\frac{1}{2}c\right) for c.

$$c=-5$$

Substitute -5 for c in the equation b=-\frac{11}{2}-\frac{1}{2}c.

$$b=-\frac{11}{2}-\frac{1}{2}\left(-5\right)$$

Calculate b from b=-\frac{11}{2}-\frac{1}{2}\left(-5\right).

$$b=-3$$

Substitute -3 for b and -5 for c in the equation a=-b-c-7.

$$a=-\left(-3\right)-\left(-5\right)-7$$

Calculate a from a=-\left(-3\right)-\left(-5\right)-7.

$$a=1$$

The system is now solved.

$$a=1 b=-3 c=-5$$