Solve {l}{-a+4b+2c=-8}{3a+b-4c=9}{b=-1}

$$\left. \begin{array}{l}{ - a + 4 b + 2 c = - 8 }\\{ 3 a + b - 4 c = 9 }\\{ b = - 1 }\end{array} \right.$$

Solve for a, b, c

$$a=2$$

$$b=-1$$

$$c=-1$$

Short Steps Using Substitution

Reorder the equations.

$$b=-1 3a+b-4c=9 -a+4b+2c=-8$$

Substitute -1 for b in the second and third equation.

$$3a-1-4c=9 -a+4\left(-1\right)+2c=-8$$

Solve these equations for a and c respectively.

$$a=\frac{10}{3}+\frac{4}{3}c c=\frac{1}{2}a-2$$

Substitute \frac{10}{3}+\frac{4}{3}c for a in the equation c=\frac{1}{2}a-2.

$$c=\frac{1}{2}\left(\frac{10}{3}+\frac{4}{3}c\right)-2$$

Solve c=\frac{1}{2}\left(\frac{10}{3}+\frac{4}{3}c\right)-2 for c.

$$c=-1$$

Substitute -1 for c in the equation a=\frac{10}{3}+\frac{4}{3}c.

$$a=\frac{10}{3}+\frac{4}{3}\left(-1\right)$$

Calculate a from a=\frac{10}{3}+\frac{4}{3}\left(-1\right).

$$a=2$$

The system is now solved.

$$a=2 b=-1 c=-1$$