Solve {l}{0=16a-4b+1}{-4=c}{0=4a+2b+c}

$$\left\{ \begin{array} { l } { 0 = 16 a - 4 b + 1 } \\ { - 4 = c } \\ { 0 = 4 a + 2 b + c } \end{array} \right.$$

Solve for a, b, c

$$a=\frac{7}{24}\approx 0.291666667$$

$$b = \frac{17}{12} = 1\frac{5}{12} \approx 1.416666667$$

$$c=-4$$

Short Steps Using Substitution

Reorder the equations.

$$-4=c 0=16a-4b+1 0=4a+2b+c$$

Solve -4=c for c.

$$c=-4$$

Substitute -4 for c in the equation 0=4a+2b+c.

$$0=4a+2b-4$$

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

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

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

$$a=1-\frac{1}{2}\left(4a+\frac{1}{4}\right)$$

Solve a=1-\frac{1}{2}\left(4a+\frac{1}{4}\right) for a.

$$a=\frac{7}{24}$$

Substitute \frac{7}{24} for a in the equation b=4a+\frac{1}{4}.

$$b=4\times \frac{7}{24}+\frac{1}{4}$$

Calculate b from b=4\times \frac{7}{24}+\frac{1}{4}.

$$b=\frac{17}{12}$$

The system is now solved.

$$a=\frac{7}{24} b=\frac{17}{12} c=-4$$