Solve {l}{6.65A+2.705=806.10}{7A+S=202}

$$\left\{ \begin{array} { l } { 6.65 A + 2.705 = 806.10 } \\ { 7 A + S = 202 } \end{array} \right.$$

Solve for A, S

$$A = \frac{160679}{1330} = 120\frac{1079}{1330} \approx 120.811278195$$

$$S = -\frac{122299}{190} = -643\frac{129}{190} \approx -643.678947368$$

Solution Steps

Consider the first equation. Subtract 2.705 from both sides.

$$6.65A=806.1-2.705$$

Subtract 2.705 from 806.1 to get 803.395.

$$6.65A=803.395$$

Divide both sides by 6.65.

$$A=\frac{803.395}{6.65}$$

Expand \frac{803.395}{6.65} by multiplying both numerator and the denominator by 1000.

$$A=\frac{803395}{6650}$$

Reduce the fraction \frac{803395}{6650} to lowest terms by extracting and canceling out 5.

$$A=\frac{160679}{1330}$$

Consider the second equation. Insert the known values of variables into the equation.

$$7\times \frac{160679}{1330}+S=202$$

Multiply 7 and \frac{160679}{1330} to get \frac{160679}{190}.

$$\frac{160679}{190}+S=202$$

Subtract \frac{160679}{190} from both sides.

$$S=202-\frac{160679}{190}$$

Subtract \frac{160679}{190} from 202 to get -\frac{122299}{190}.

$$S=-\frac{122299}{190}$$

The system is now solved.

$$A=\frac{160679}{1330} S=-\frac{122299}{190}$$