Solve {l}{9a-3b+c=-2}{a-b+c=-14}{4a-2b+c=-7}

$$\left. \begin{array} { l } { 9 a - 3 b + c = - 2 } \\ { a - b + c = - 14 } \\ { 4 a - 2 b + c = - 7 } \end{array} \right.$$

Solve for a, b, c

$$a=-1$$

$$b=-10$$

$$c=-23$$

Short Steps Using Substitution

Solve 9a-3b+c=-2 for c.

$$c=-9a+3b-2$$

Substitute -9a+3b-2 for c in the second and third equation.

$$a-b-9a+3b-2=-14 4a-2b-9a+3b-2=-7$$

Solve these equations for b and a respectively.

$$b=-6+4a a=\frac{1}{5}b+1$$

Substitute -6+4a for b in the equation a=\frac{1}{5}b+1.

$$a=\frac{1}{5}\left(-6+4a\right)+1$$

Solve a=\frac{1}{5}\left(-6+4a\right)+1 for a.

$$a=-1$$

Substitute -1 for a in the equation b=-6+4a.

$$b=-6+4\left(-1\right)$$

Calculate b from b=-6+4\left(-1\right).

$$b=-10$$

Substitute -10 for b and -1 for a in the equation c=-9a+3b-2.

$$c=-9\left(-1\right)+3\left(-10\right)-2$$

Calculate c from c=-9\left(-1\right)+3\left(-10\right)-2.

$$c=-23$$

The system is now solved.

$$a=-1 b=-10 c=-23$$