Solve {l}{-1.25a+b+1.25c=0}{-a+3b=60}{a-3c=24}

$$\left. \begin{array} { l } { - 1.25 a + b + 1.25 c = 0 } \\ { - a + 3 b = 60 } \\ { a - 3 c = 24 } \end{array} \right.$$

Solve for a, b, c

$$a=20$$

$$b = \frac{80}{3} = 26\frac{2}{3} \approx 26.666666667$$

$$c = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Short Steps Using Substitution

Solve -1.25a+b+1.25c=0 for b.

$$b=1.25a-1.25c$$

Substitute 1.25a-1.25c for b in the equation -a+3b=60.

$$-a+3\left(1.25a-1.25c\right)=60$$

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

$$a=\frac{15}{11}c+\frac{240}{11} c=\frac{1}{3}a-8$$

Substitute \frac{15}{11}c+\frac{240}{11} for a in the equation c=\frac{1}{3}a-8.

$$c=\frac{1}{3}\left(\frac{15}{11}c+\frac{240}{11}\right)-8$$

Solve c=\frac{1}{3}\left(\frac{15}{11}c+\frac{240}{11}\right)-8 for c.

$$c=-\frac{4}{3}$$

Substitute -\frac{4}{3} for c in the equation a=\frac{15}{11}c+\frac{240}{11}.

$$a=\frac{15}{11}\left(-\frac{4}{3}\right)+\frac{240}{11}$$

Calculate a from a=\frac{15}{11}\left(-\frac{4}{3}\right)+\frac{240}{11}.

$$a=20$$

Substitute 20 for a and -\frac{4}{3} for c in the equation b=1.25a-1.25c.

$$b=1.25\times 20-1.25\left(-\frac{4}{3}\right)$$

Calculate b from b=1.25\times 20-1.25\left(-\frac{4}{3}\right).

$$b=\frac{80}{3}$$

The system is now solved.

$$a=20 b=\frac{80}{3} c=-\frac{4}{3}$$