Solve {l}{99(6a+6)=22}{99(2a+b)=24}

$$\left\{ \begin{array} { l } { 99 ( 6 a + 6 ) = 22 } \\ { 99 ( 2 a + b ) = 24 } \end{array} \right.$$

Solve for a, b

$$a=-\frac{26}{27}\approx -0.962962963$$

$$b = \frac{644}{297} = 2\frac{50}{297} \approx 2.168350168$$

Solution Steps

Consider the first equation. Divide both sides by 99.

$$6a+6=\frac{22}{99}$$

Reduce the fraction \frac{22}{99} to lowest terms by extracting and canceling out 11.

$$6a+6=\frac{2}{9}$$

Subtract 6 from both sides.

$$6a=\frac{2}{9}-6$$

Subtract 6 from \frac{2}{9} to get -\frac{52}{9}.

$$6a=-\frac{52}{9}$$

Divide both sides by 6.

$$a=\frac{-\frac{52}{9}}{6}$$

Express \frac{-\frac{52}{9}}{6} as a single fraction.

$$a=\frac{-52}{9\times 6}$$

Multiply 9 and 6 to get 54.

$$a=\frac{-52}{54}$$

Reduce the fraction \frac{-52}{54} to lowest terms by extracting and canceling out 2.

$$a=-\frac{26}{27}$$

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

$$99\left(2\left(-\frac{26}{27}\right)+b\right)=24$$

Divide both sides by 99.

$$2\left(-\frac{26}{27}\right)+b=\frac{24}{99}$$

Reduce the fraction \frac{24}{99} to lowest terms by extracting and canceling out 3.

$$2\left(-\frac{26}{27}\right)+b=\frac{8}{33}$$

Multiply 2 and -\frac{26}{27} to get -\frac{52}{27}.

$$-\frac{52}{27}+b=\frac{8}{33}$$

Add \frac{52}{27} to both sides.

$$b=\frac{8}{33}+\frac{52}{27}$$

Add \frac{8}{33} and \frac{52}{27} to get \frac{644}{297}.

$$b=\frac{644}{297}$$

The system is now solved.

$$a=-\frac{26}{27} b=\frac{644}{297}$$