Solve {l}{24.5-9a=8a5-25a}{24.5+76a=80.5}

$$\left. \begin{array} { l } { 24.5 - 9 a = 8 a 5 - 25 a } \\ { 24.5 + 76 a = 80.5 } \end{array} \right.$$

Solve for a, a_5

$$a=\frac{14}{19}\approx 0.736842105$$

$$a_{5} = \frac{1379}{304} = 4\frac{163}{304} \approx 4.536184211$$

Solution Steps

Consider the second equation. Subtract 24.5 from both sides.

$$76a=80.5-24.5$$

Subtract 24.5 from 80.5 to get 56.

$$76a=56$$

Divide both sides by 76.

$$a=\frac{56}{76}$$

Reduce the fraction \frac{56}{76} to lowest terms by extracting and canceling out 4.

$$a=\frac{14}{19}$$

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

$$24.5-9\times \frac{14}{19}=8a_{5}-25\times \frac{14}{19}$$

Multiply -9 and \frac{14}{19} to get -\frac{126}{19}.

$$24.5-\frac{126}{19}=8a_{5}-25\times \frac{14}{19}$$

Subtract \frac{126}{19} from 24.5 to get \frac{679}{38}.

$$\frac{679}{38}=8a_{5}-25\times \frac{14}{19}$$

Multiply -25 and \frac{14}{19} to get -\frac{350}{19}.

$$\frac{679}{38}=8a_{5}-\frac{350}{19}$$

Swap sides so that all variable terms are on the left hand side.

$$8a_{5}-\frac{350}{19}=\frac{679}{38}$$

Add \frac{350}{19} to both sides.

$$8a_{5}=\frac{679}{38}+\frac{350}{19}$$

Add \frac{679}{38} and \frac{350}{19} to get \frac{1379}{38}.

$$8a_{5}=\frac{1379}{38}$$

Divide both sides by 8.

$$a_{5}=\frac{\frac{1379}{38}}{8}$$

Express \frac{\frac{1379}{38}}{8} as a single fraction.

$$a_{5}=\frac{1379}{38\times 8}$$

Multiply 38 and 8 to get 304.

$$a_{5}=\frac{1379}{304}$$

The system is now solved.

$$a=\frac{14}{19} a_{5}=\frac{1379}{304}$$