Solve {l}{a+2b+3c=4}{5a+6b+c=7}{8a+9b+}{10c=100}

$$\left. \begin{array} { l } { a + 2 b + 3 c = 4 } \\ { 5 a + 6 b + c = 7 } \\ { 8 a + 9 b + } \\ { 10 c = 100 } \end{array} \right.$$

Solve for a, b, c

$$a = \frac{75}{2} = 37\frac{1}{2} = 37.5$$

$$b = -\frac{127}{4} = -31\frac{3}{4} = -31.75$$

$$c=10$$

Short Steps Using Substitution

Solve a+2b+3c=4 for a.

$$a=-2b-3c+4$$

Substitute -2b-3c+4 for a in the equation 5a+6b+c=7.

$$5\left(-2b-3c+4\right)+6b+c=7$$

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

$$b=-\frac{7}{2}c+\frac{13}{4} c=10$$

Substitute 10 for c in the equation b=-\frac{7}{2}c+\frac{13}{4}.

$$b=-\frac{7}{2}\times 10+\frac{13}{4}$$

Calculate b from b=-\frac{7}{2}\times 10+\frac{13}{4}.

$$b=-\frac{127}{4}$$

Substitute -\frac{127}{4} for b and 10 for c in the equation a=-2b-3c+4.

$$a=-2\left(-\frac{127}{4}\right)-3\times 10+4$$

Calculate a from a=-2\left(-\frac{127}{4}\right)-3\times 10+4.

$$a=\frac{75}{2}$$

The system is now solved.

$$a=\frac{75}{2} b=-\frac{127}{4} c=10$$