Solve {l}{a-b-6=-3}{-2+b+2c=-1}{a-3-2c=-3}

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

Solve for a, b, c

$$a=2$$

$$b=-1$$

$$c=1$$

Short Steps Using Substitution

Solve a-b-6=-3 for a.

$$a=b+3$$

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

$$b+3-3-2c=-3$$

Solve the second equation for b and the third equation for c.

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

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

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

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

$$c=1$$

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

$$b=1-2$$

Calculate b from b=1-2.

$$b=-1$$

Substitute -1 for b in the equation a=b+3.

$$a=-1+3$$

Calculate a from a=-1+3.

$$a=2$$

The system is now solved.

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