Solve {l}{9.1=100a+10b+c}{7.9=900a+30b+c}{10=10000a+100b+c}

$$\left\{ \begin{array} { l } { 9.1 = 100 a + 10 b + c } \\ { 7.9 = 900 a + 30 b + c } \\ { 10 = 10000 a + 100 b + c } \end{array} \right.$$

Solve for a, b, c

$$a=0.001$$

$$b=-0.1$$

$$c=10$$

Short Steps Using Substitution

Solve 9.1=100a+10b+c for c.

$$c=-100a+9.1-10b$$

Substitute -100a+9.1-10b for c in the second and third equation.

$$7.9=900a+30b-100a+9.1-10b 10=10000a+100b-100a+9.1-10b$$

Solve these equations for b and a respectively.

$$b=-\frac{3}{50}-40a a=\frac{1}{11000}-\frac{1}{110}b$$

Substitute -\frac{3}{50}-40a for b in the equation a=\frac{1}{11000}-\frac{1}{110}b.

$$a=\frac{1}{11000}-\frac{1}{110}\left(-\frac{3}{50}-40a\right)$$

Solve a=\frac{1}{11000}-\frac{1}{110}\left(-\frac{3}{50}-40a\right) for a.

$$a=0.001$$

Substitute 0.001 for a in the equation b=-\frac{3}{50}-40a.

$$b=-\frac{3}{50}-40\times 0.001$$

Calculate b from b=-\frac{3}{50}-40\times 0.001.

$$b=-0.1$$

Substitute -0.1 for b and 0.001 for a in the equation c=-100a+9.1-10b.

$$c=-100\times 0.001+9.1-10\left(-0.1\right)$$

Calculate c from c=-100\times 0.001+9.1-10\left(-0.1\right).

$$c=10$$

The system is now solved.

$$a=0.001 b=-0.1 c=10$$