Solve {l}{c=6}{0=4a-2b+c}{a=9a+3b+c}

$$\left\{ \begin{array} { l } { c = 6 } \\ { 0 = 4 a - 2 b + c } \\ { a = 9 a + 3 b + c } \end{array} \right.$$

Solve for c, a, b

$$c=6$$

$$a = -\frac{15}{14} = -1\frac{1}{14} \approx -1.071428571$$

$$b=\frac{6}{7}\approx 0.857142857$$

Short Steps Using Substitution

Substitute 6 for c in the second and third equation.

$$0=4a-2b+6 a=9a+3b+6$$

Solve these equations for a and b respectively.

$$a=-\frac{3}{2}+\frac{1}{2}b b=-2-\frac{8}{3}a$$

Substitute -\frac{3}{2}+\frac{1}{2}b for a in the equation b=-2-\frac{8}{3}a.

$$b=-2-\frac{8}{3}\left(-\frac{3}{2}+\frac{1}{2}b\right)$$

Solve b=-2-\frac{8}{3}\left(-\frac{3}{2}+\frac{1}{2}b\right) for b.

$$b=\frac{6}{7}$$

Substitute \frac{6}{7} for b in the equation a=-\frac{3}{2}+\frac{1}{2}b.

$$a=-\frac{3}{2}+\frac{1}{2}\times \frac{6}{7}$$

Calculate a from a=-\frac{3}{2}+\frac{1}{2}\times \frac{6}{7}.

$$a=-\frac{15}{14}$$

The system is now solved.

$$c=6 a=-\frac{15}{14} b=\frac{6}{7}$$