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

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

Solve for a, b, c

$$a=1$$

$$b=-2$$

$$c=-3$$

Short Steps Using Substitution

Solve 0=a-b+c for a.

$$a=b-c$$

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

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

Solve these equations for b and c respectively.

$$b=-2 c=1+2b$$

Substitute -2 for b in the equation c=1+2b.

$$c=1+2\left(-2\right)$$

Calculate c from c=1+2\left(-2\right).

$$c=-3$$

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

$$a=-2-\left(-3\right)$$

Calculate a from a=-2-\left(-3\right).

$$a=1$$

The system is now solved.

$$a=1 b=-2 c=-3$$