Solve {l}{a+5.00b+3.20c=6}{a+3.50b+1.95c=4}{a+5.00b+5.20c=8}

$$\left. \begin{array} { l } { a + 5.00 b + 3.20 c = 6 } \\ { a + 3.50 b + 1.95 c = 4 } \\ { a + 5.00 b + 5.20 c = 8 } \end{array} \right.$$

Solve for a, b, c

$$a=0.3$$

$$b=0.5$$

$$c=1$$

Short Steps Using Substitution

Solve a+5b+3.2c=6 for a.

$$a=-5b-3.2c+6$$

Substitute -5b-3.2c+6 for a in the second and third equation.

$$-5b-3.2c+6+3.5b+1.95c=4 -5b-3.2c+6+5b+5.2c=8$$

Solve these equations for b and c respectively.

$$b=-\frac{5}{6}c+\frac{4}{3} c=1$$

Substitute 1 for c in the equation b=-\frac{5}{6}c+\frac{4}{3}.

$$b=-\frac{5}{6}+\frac{4}{3}$$

Calculate b from b=-\frac{5}{6}+\frac{4}{3}.

$$b=0.5$$

Substitute 0.5 for b and 1 for c in the equation a=-5b-3.2c+6.

$$a=-5\times 0.5-3.2+6$$

Calculate a from a=-5\times 0.5-3.2+6.

$$a=0.3$$

The system is now solved.

$$a=0.3 b=0.5 c=1$$