Solve {c}{-14.75a+6b=-37.5}{3a-8b=32.5}{-3b+6c=19.5}

$$\left. \begin{array} { c } { - 14.75 a + 6 b = - 37.5 } \\ { 3 a - 8 b = 32.5 } \\ { - 3 b + 6 c = 19.5 } \end{array} \right.$$

Solve for a, b, c

$$a=1.05$$

$$b=-3.66875$$

$$c=1.415625$$

Short Steps Using Substitution

Solve -14.75a+6b=-37.5 for a.

$$a=\frac{24}{59}b+\frac{150}{59}$$

Substitute \frac{24}{59}b+\frac{150}{59} for a in the equation 3a-8b=32.5.

$$3\left(\frac{24}{59}b+\frac{150}{59}\right)-8b=32.5$$

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

$$b=-\frac{587}{160} c=\frac{1}{2}b+\frac{13}{4}$$

Substitute -\frac{587}{160} for b in the equation c=\frac{1}{2}b+\frac{13}{4}.

$$c=\frac{1}{2}\left(-\frac{587}{160}\right)+\frac{13}{4}$$

Calculate c from c=\frac{1}{2}\left(-\frac{587}{160}\right)+\frac{13}{4}.

$$c=\frac{453}{320}$$

Substitute -\frac{587}{160} for b in the equation a=\frac{24}{59}b+\frac{150}{59}.

$$a=\frac{24}{59}\left(-\frac{587}{160}\right)+\frac{150}{59}$$

Calculate a from a=\frac{24}{59}\left(-\frac{587}{160}\right)+\frac{150}{59}.

$$a=\frac{21}{20}$$

The system is now solved.

$$a=\frac{21}{20} b=-\frac{587}{160} c=\frac{453}{320}$$