Solve {l}{2a-5c-15=0}{5c+4b+8b=0}{a+c-b=0}

$$\left. \begin{array} { l } { 2 a - 5 c - 15 = 0 } \\ { 5 c + 4 b + 8 b = 0 } \\ { a + c - b = 0 } \end{array} \right.$$

Solve for a, c, b

$$a = \frac{255}{94} = 2\frac{67}{94} \approx 2.712765957$$

$$c = -\frac{90}{47} = -1\frac{43}{47} \approx -1.914893617$$

$$b=\frac{75}{94}\approx 0.79787234$$

Short Steps Using Substitution

Reorder the equations.

$$a+c-b=0 5c+4b+8b=0 2a-5c-15=0$$

Solve a+c-b=0 for a.

$$a=-c+b$$

Substitute -c+b for a in the equation 2a-5c-15=0.

$$2\left(-c+b\right)-5c-15=0$$

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

$$c=-\frac{12}{5}b b=\frac{15}{2}+\frac{7}{2}c$$

Substitute -\frac{12}{5}b for c in the equation b=\frac{15}{2}+\frac{7}{2}c.

$$b=\frac{15}{2}+\frac{7}{2}\left(-\frac{12}{5}\right)b$$

Solve b=\frac{15}{2}+\frac{7}{2}\left(-\frac{12}{5}\right)b for b.

$$b=\frac{75}{94}$$

Substitute \frac{75}{94} for b in the equation c=-\frac{12}{5}b.

$$c=-\frac{12}{5}\times \frac{75}{94}$$

Calculate c from c=-\frac{12}{5}\times \frac{75}{94}.

$$c=-\frac{90}{47}$$

Substitute -\frac{90}{47} for c and \frac{75}{94} for b in the equation a=-c+b.

$$a=-\left(-\frac{90}{47}\right)+\frac{75}{94}$$

Calculate a from a=-\left(-\frac{90}{47}\right)+\frac{75}{94}.

$$a=\frac{255}{94}$$

The system is now solved.

$$a=\frac{255}{94} c=-\frac{90}{47} b=\frac{75}{94}$$