Solve {l}{25/4a+5/2b+c=15/8}{49/4a+frac{7}{2}b+c=frac{7}{8}}{16a+4b+c=0}

$$\left\{ \begin{array} { l } { \frac { 25 } { 4 } a + \frac { 5 } { 2 } b + c = \frac { 15 } { 8 } } \\ { \frac { 49 } { 4 } a + \frac { 7 } { 2 } b + c = \frac { 7 } { 8 } } \\ { 16 a + 4 b + c = 0 } \end{array} \right.$$

Solve for a, b, c

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

$$b=2$$

$$c=0$$

Short Steps Using Substitution

Solve \frac{25}{4}a+\frac{5}{2}b+c=\frac{15}{8} for c.

$$c=\frac{15}{8}-\frac{25}{4}a-\frac{5}{2}b$$

Substitute \frac{15}{8}-\frac{25}{4}a-\frac{5}{2}b for c in the second and third equation.

$$\frac{49}{4}a+\frac{7}{2}b+\frac{15}{8}-\frac{25}{4}a-\frac{5}{2}b=\frac{7}{8} 16a+4b+\frac{15}{8}-\frac{25}{4}a-\frac{5}{2}b=0$$

Solve these equations for b and a respectively.

$$b=-6a-1 a=-\frac{5}{26}-\frac{2}{13}b$$

Substitute -6a-1 for b in the equation a=-\frac{5}{26}-\frac{2}{13}b.

$$a=-\frac{5}{26}-\frac{2}{13}\left(-6a-1\right)$$

Solve a=-\frac{5}{26}-\frac{2}{13}\left(-6a-1\right) for a.

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

Substitute -\frac{1}{2} for a in the equation b=-6a-1.

$$b=-6\left(-\frac{1}{2}\right)-1$$

Calculate b from b=-6\left(-\frac{1}{2}\right)-1.

$$b=2$$

Substitute 2 for b and -\frac{1}{2} for a in the equation c=\frac{15}{8}-\frac{25}{4}a-\frac{5}{2}b.

$$c=\frac{15}{8}-\frac{25}{4}\left(-\frac{1}{2}\right)-\frac{5}{2}\times 2$$

Calculate c from c=\frac{15}{8}-\frac{25}{4}\left(-\frac{1}{2}\right)-\frac{5}{2}\times 2.

$$c=0$$

The system is now solved.

$$a=-\frac{1}{2} b=2 c=0$$