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

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

Solve for a, b, c

$$a=1$$

$$b=6$$

$$c=9$$

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.

$$-8\left(b-c+4\right)+4b-2c=-2 3\left(b-c+4\right)-2b+c=0$$

Solve these equations for b and c respectively.

$$b=-\frac{15}{2}+\frac{3}{2}c c=\frac{1}{2}b+6$$

Substitute -\frac{15}{2}+\frac{3}{2}c for b in the equation c=\frac{1}{2}b+6.

$$c=\frac{1}{2}\left(-\frac{15}{2}+\frac{3}{2}c\right)+6$$

Solve c=\frac{1}{2}\left(-\frac{15}{2}+\frac{3}{2}c\right)+6 for c.

$$c=9$$

Substitute 9 for c in the equation b=-\frac{15}{2}+\frac{3}{2}c.

$$b=-\frac{15}{2}+\frac{3}{2}\times 9$$

Calculate b from b=-\frac{15}{2}+\frac{3}{2}\times 9.

$$b=6$$

Substitute 6 for b and 9 for c in the equation a=b-c+4.

$$a=6-9+4$$

Calculate a from a=6-9+4.

$$a=1$$

The system is now solved.

$$a=1 b=6 c=9$$