Solve {l}{1,2a+13-0,9a+0,5=16,7-0,}{7,0,4-1,6n=3,2n-0,08}

$$\left. \begin{array} { l } { 1,2 a + 13 - 0,9 a + 0,5 = 16,7 - 0 , } \\ { 7,0,4 - 1,6 n = 3,2 n - 0,08 } \end{array} \right.$$

Solve for a, n

$$a = \frac{32}{3} = 10\frac{2}{3} \approx 10.666666667$$

$$n=5.85$$

Solution Steps

Consider the first equation. Combine 1.2a and -0.9a to get 0.3a.

$$0.3a+13+0.5=16.7-0$$

Add 13 and 0.5 to get 13.5.

$$0.3a+13.5=16.7-0$$

Subtract 0 from 16.7 to get 16.7.

$$0.3a+13.5=16.7$$

Subtract 13.5 from both sides.

$$0.3a=16.7-13.5$$

Subtract 13.5 from 16.7 to get 3.2.

$$0.3a=3.2$$

Divide both sides by 0.3.

$$a=\frac{3.2}{0.3}$$

Expand \frac{3.2}{0.3} by multiplying both numerator and the denominator by 10.

$$a=\frac{32}{3}$$

Consider the second equation. Multiply 7 and 4 to get 28.

$$28-1.6n=3.2n-0.08$$

Subtract 3.2n from both sides.

$$28-1.6n-3.2n=-0.08$$

Combine -1.6n and -3.2n to get -4.8n.

$$28-4.8n=-0.08$$

Subtract 28 from both sides.

$$-4.8n=-0.08-28$$

Subtract 28 from -0.08 to get -28.08.

$$-4.8n=-28.08$$

Divide both sides by -4.8.

$$n=\frac{-28.08}{-4.8}$$

Expand \frac{-28.08}{-4.8} by multiplying both numerator and the denominator by 100.

$$n=\frac{-2808}{-480}$$

Reduce the fraction \frac{-2808}{-480} to lowest terms by extracting and canceling out -24.

$$n=\frac{117}{20}$$

The system is now solved.

$$a=\frac{32}{3} n=\frac{117}{20}$$