Solve {l}{5=25a+5b+c}{2=100a+10b+c}{2=c}

$$\left. \begin{array} { l } { 5 = 25 a + 5 b + c } \\ { 2 = 100 a + 10 b + c } \\ { 2 = c } \end{array} \right.$$

Solve for a, b, c

$$a=-\frac{3}{25}=-0.12$$

$$b = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$c=2$$

Short Steps Using Substitution

Reorder the equations.

$$2=c 2=100a+10b+c 5=25a+5b+c$$

Solve 2=c for c.

$$c=2$$

Substitute 2 for c in the second and third equation.

$$2=100a+10b+2 5=25a+5b+2$$

Solve these equations for b and a respectively.

$$b=-10a a=-\frac{1}{5}b+\frac{3}{25}$$

Substitute -10a for b in the equation a=-\frac{1}{5}b+\frac{3}{25}.

$$a=-\frac{1}{5}\left(-10\right)a+\frac{3}{25}$$

Solve a=-\frac{1}{5}\left(-10\right)a+\frac{3}{25} for a.

$$a=-\frac{3}{25}$$

Substitute -\frac{3}{25} for a in the equation b=-10a.

$$b=-10\left(-\frac{3}{25}\right)$$

Calculate b from b=-10\left(-\frac{3}{25}\right).

$$b=\frac{6}{5}$$

The system is now solved.

$$a=-\frac{3}{25} b=\frac{6}{5} c=2$$