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

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

Solve for b, c, a

$$b = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$c = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$a = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Short Steps Using Substitution

Solve -b+c=2 for b.

$$b=c-2$$

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

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

Solve these equations for c and a respectively.

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

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

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

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

$$a=-\frac{5}{2}$$

Substitute -\frac{5}{2} for a in the equation c=-\frac{1}{3}a+\frac{8}{3}.

$$c=-\frac{1}{3}\left(-\frac{5}{2}\right)+\frac{8}{3}$$

Calculate c from c=-\frac{1}{3}\left(-\frac{5}{2}\right)+\frac{8}{3}.

$$c=\frac{7}{2}$$

Substitute \frac{7}{2} for c in the equation b=c-2.

$$b=\frac{7}{2}-2$$

Calculate b from b=\frac{7}{2}-2.

$$b=\frac{3}{2}$$

The system is now solved.

$$b=\frac{3}{2} c=\frac{7}{2} a=-\frac{5}{2}$$