Solve {l}{2a+3b+c=0}{4a-3b-c=1}{7a-8b+6c=1}

$$\left. \begin{array} { l } { 2 a + 3 b + c = 0 } \\ { 4 a - 3 b - c = 1 } \\ { 7 a - 8 b + 6 c = 1 } \end{array} \right.$$

Solve for a, b, c

$$a=\frac{1}{6}\approx 0.166666667$$

$$b=-\frac{11}{156}\approx -0.070512821$$

$$c=-\frac{19}{156}\approx -0.121794872$$

Short Steps Using Substitution

Solve 2a+3b+c=0 for c.

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

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

$$4a-3b-\left(-2a-3b\right)=1 7a-8b+6\left(-2a-3b\right)=1$$

Solve these equations for a and b respectively.

$$a=\frac{1}{6} b=-\frac{5}{26}a-\frac{1}{26}$$

Substitute \frac{1}{6} for a in the equation b=-\frac{5}{26}a-\frac{1}{26}.

$$b=-\frac{5}{26}\times \frac{1}{6}-\frac{1}{26}$$

Calculate b from b=-\frac{5}{26}\times \frac{1}{6}-\frac{1}{26}.

$$b=-\frac{11}{156}$$

Substitute \frac{1}{6} for a and -\frac{11}{156} for b in the equation c=-2a-3b.

$$c=-2\times \frac{1}{6}-3\left(-\frac{11}{156}\right)$$

Calculate c from c=-2\times \frac{1}{6}-3\left(-\frac{11}{156}\right).

$$c=-\frac{19}{156}$$

The system is now solved.

$$a=\frac{1}{6} b=-\frac{11}{156} c=-\frac{19}{156}$$