Solve {l}{a-b+c=0}{16a+4b+c=5/2}{c=-3/2}

$$\left\{ \begin{array} { l } { a - b + c = 0 } \\ { 16 a + 4 b + c = \frac { 5 } { 2 } } \\ { c = - \frac { 3 } { 2 } } \end{array} \right.$$

Solve for a, b, c

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

$$b=-1$$

$$c = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Short Steps Using Substitution

Reorder the equations.

$$c=-\frac{3}{2} 16a+4b+c=\frac{5}{2} a-b+c=0$$

Substitute -\frac{3}{2} for c in the second and third equation.

$$16a+4b-\frac{3}{2}=\frac{5}{2} a-b-\frac{3}{2}=0$$

Solve these equations for b and a respectively.

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

Substitute 1-4a for b in the equation a=b+\frac{3}{2}.

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

Solve a=1-4a+\frac{3}{2} for a.

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

Substitute \frac{1}{2} for a in the equation b=1-4a.

$$b=1-4\times \frac{1}{2}$$

Calculate b from b=1-4\times \frac{1}{2}.

$$b=-1$$

The system is now solved.

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