Solve {l}{9.1=100a+106+c}{7.9=900a+306+c}{10=10000a+100b+c}

$$\left\{ \begin{array} { l } { 9.1 = 100 a + 106 + c } \\ { 7.9 = 900 a + 306 + c } \\ { 10 = 10000 a + 100 b + c } \end{array} \right.$$

Solve for a, c, b

$$a=-0.2515$$

$$c=-71.75$$

$$b=25.9675$$

Short Steps Using Substitution

Solve 9.1=100a+106+c for c.

$$c=-100a-\frac{969}{10}$$

Substitute -100a-\frac{969}{10} for c in the second and third equation.

$$7.9=900a+306-100a-\frac{969}{10} 10=10000a+100b-100a-\frac{969}{10}$$

Solve these equations for a and b respectively.

$$a=-0.2515 b=-99a+\frac{1069}{1000}$$

Substitute -0.2515 for a in the equation b=-99a+\frac{1069}{1000}.

$$b=-99\left(-0.2515\right)+\frac{1069}{1000}$$

Calculate b from b=-99\left(-0.2515\right)+\frac{1069}{1000}.

$$b=\frac{10387}{400}$$

Substitute -0.2515 for a in the equation c=-100a-\frac{969}{10}.

$$c=-100\left(-0.2515\right)-\frac{969}{10}$$

Calculate c from c=-100\left(-0.2515\right)-\frac{969}{10}.

$$c=-71.75$$

The system is now solved.

$$a=-0.2515 c=-71.75 b=\frac{10387}{400}$$