Solve {l}{4a+2b+c=3-6}{a-b+c=6}{9a+3b+c=6}

$$\left\{ \begin{array} { l } { 4 a + 2 b + c = 3 - 6 } \\ { a - b + c = 6 } \\ { 9 a + 3 b + c = 6 } \end{array} \right.$$

Solve for a, b, c

$$a=3$$

$$b=-6$$

$$c=-3$$

Short Steps Using Substitution

Solve 4a+2b+c=3-6 for c.

$$c=-4a-2b-3$$

Substitute -4a-2b-3 for c in the second and third equation.

$$a-b-4a-2b-3=6 9a+3b-4a-2b-3=6$$

Solve these equations for b and a respectively.

$$b=-3-a a=-\frac{1}{5}b+\frac{9}{5}$$

Substitute -3-a for b in the equation a=-\frac{1}{5}b+\frac{9}{5}.

$$a=-\frac{1}{5}\left(-3-a\right)+\frac{9}{5}$$

Solve a=-\frac{1}{5}\left(-3-a\right)+\frac{9}{5} for a.

$$a=3$$

Substitute 3 for a in the equation b=-3-a.

$$b=-3-3$$

Calculate b from b=-3-3.

$$b=-6$$

Substitute -6 for b and 3 for a in the equation c=-4a-2b-3.

$$c=-4\times 3-2\left(-6\right)-3$$

Calculate c from c=-4\times 3-2\left(-6\right)-3.

$$c=-3$$

The system is now solved.

$$a=3 b=-6 c=-3$$