Solve {l}{9a-3b+c=-5/2}{4a-2b+c=-4}{a-1+c=-9/2}

$$\left. \begin{array} { l } { 9 a - 3 b + c = - \frac { 5 } { 2 } } \\ { 4 a - 2 b + c = - 4 } \\ { a - 1 + c = - \frac { 9 } { 2 } } \end{array} \right.$$

Solve for a, b, c

$$a=\frac{1}{2}=0.5$$

$$b=1$$

$$c=-4$$

Short Steps Using Substitution

Solve 9a-3b+c=-\frac{5}{2} for c.

$$c=-9a+3b-\frac{5}{2}$$

Substitute -9a+3b-\frac{5}{2} for c in the second and third equation.

$$4a-2b-9a+3b-\frac{5}{2}=-4 a-1-9a+3b-\frac{5}{2}=-\frac{9}{2}$$

Solve these equations for b and a respectively.

$$b=5a-\frac{3}{2} a=\frac{1}{8}+\frac{3}{8}b$$

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

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

Solve a=\frac{1}{8}+\frac{3}{8}\left(5a-\frac{3}{2}\right) for a.

$$a=\frac{1}{2}$$

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

$$b=5\times \frac{1}{2}-\frac{3}{2}$$

Calculate b from b=5\times \frac{1}{2}-\frac{3}{2}.

$$b=1$$

Substitute 1 for b and \frac{1}{2} for a in the equation c=-9a+3b-\frac{5}{2}.

$$c=-9\times \frac{1}{2}+3\times 1-\frac{5}{2}$$

Calculate c from c=-9\times \frac{1}{2}+3\times 1-\frac{5}{2}.

$$c=-4$$

The system is now solved.

$$a=\frac{1}{2} b=1 c=-4$$